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Circle Theorems · MCQ assessment
Version A
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
/ 15
1$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 28^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe angle in a semicircle is 90°BOpposite angles of a cyclic quadrilateral add up to 180°CBase angles of an isosceles triangle are equalDThe angle at the centre is twice the angle at the circumference
2In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. Angle $ACB = 41^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe angle in a semicircle is 90°BAngles in the same segment are equalCThe angle at the centre is twice the angle at the circumferenceDA tangent meets a radius at 90°
3From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 46^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in a triangle add up to 180°BThe two tangents from a point are equal in lengthCBase angles of an isosceles triangle are equalDA tangent meets a radius at 90°
4$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle DAB $= 81^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in the same segment are equalBOpposite angles of a cyclic quadrilateral add up to 180°CThe angle at the centre is twice the angle at the circumferenceDA tangent meets a radius at 90°
5In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle $ABT$ in the alternate segment is $44^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in the same segment are equalBA tangent meets a radius at 90°CThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)DBase angles of an isosceles triangle are equal
6$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CAB $= 39^\circ$. Work out the size of angle CBA, marked $x$.
A141B51C90D39
7$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle ABC $= 77^\circ$. Work out the size of angle CDA, marked $x$.
A90B77C283D103
8In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 108^\circ$. Work out the size of angle $x$.
A54B108C72D36
9$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TOP = 53^\circ$. Work out the size of angle $x$.
A90B53C127D37
10$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CAB $= 33^\circ$. Work out the size of angle CBA, marked $x$.
A57B33C147D90
11$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle ABC $= 74^\circ$. Work out the size of angle CDA, marked $x$.
A90B74C106D286
12In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle $ABT$ in the alternate segment is $56^\circ$. Work out the size of the angle between the tangent and the chord $TA$, marked $x$.
A124B56C90D112
13From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 52^\circ$. Work out the size of angle $PAB$, marked $x$.
A128B64C90D52
14In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle $ABT$ in the alternate segment is $46^\circ$. Work out the size of the angle between the tangent and the chord $TA$, marked $x$.
A92B134C46D90
15$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 43^\circ$. Work out the size of the angle $AOB$ at the centre.
A137B43C94D86
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Circle Theorems · MCQ assessment
Version B
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
/ 15
1$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 62^\circ$. Work out the size of angle $ADB$, marked $x$.
A118B62C124D90
2From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 62^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AA tangent meets a radius at 90°BThe two tangents from a point are equal in lengthCThe angle in a semicircle is 90°DBase angles of an isosceles triangle are equal
3$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle BCD $= 115^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in the same segment are equalBThe two tangents from a point are equal in lengthCOpposite angles of a cyclic quadrilateral add up to 180°DThe angle at the centre is twice the angle at the circumference
4$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TOP = 50^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)BThe two tangents from a point are equal in lengthCAngles in the same segment are equalDA tangent meets a radius at 90°
5$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 66^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe angle in a semicircle is 90°BThe angle at the centre is twice the angle at the circumferenceCOpposite angles of a cyclic quadrilateral add up to 180°DAngles in the same segment are equal
6$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TOP = 52^\circ$. Work out the size of angle $x$.
A52B90C128D38
7$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 30^\circ$. Work out the size of angle CAB, marked $x$.
A90B30C150D60
8$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle CDA $= 111^\circ$. Work out the size of angle ABC, marked $x$.
A90B249C111D69
9In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 102^\circ$. Work out the size of angle $x$.
A102B39C78D51
10$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TOP = 43^\circ$. Work out the size of angle $x$.
A137B47C43D90
11$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 57^\circ$. Work out the size of angle CAB, marked $x$.
A57B123C90D33
12From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 58^\circ$. Work out the size of angle $PAB$, marked $x$.
A122B61C90D58
13In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle between the tangent and the chord $TA$ is $56^\circ$. Work out the size of angle $ABT$ in the alternate segment, marked $x$.
A112B124C56D90
14From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 44^\circ$. Work out the size of angle $PAB$, marked $x$.
A44B68C90D136
15$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 53^\circ$. Work out the size of the angle $AOB$ at the centre.
A53B127C106D74
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Circle Theorems · MCQ assessment
Version C
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
/ 15
1In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle $ABT$ in the alternate segment is $39^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in the same segment are equalBAngles in a triangle add up to 180°CA tangent meets a radius at 90°DThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)
2From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 56^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AOpposite angles of a cyclic quadrilateral add up to 180°BThe two tangents from a point are equal in lengthCA tangent meets a radius at 90°DBase angles of an isosceles triangle are equal
3$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle ABC $= 102^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in the same segment are equalBAngles in a triangle add up to 180°COpposite angles of a cyclic quadrilateral add up to 180°DThe angle at the centre is twice the angle at the circumference
4$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 66^\circ$. Work out the size of angle $ADB$, marked $x$.
A90B132C66D114
5$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TPO = 43^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe angle at the centre is twice the angle at the circumferenceBA tangent meets a radius at 90°CThe two tangents from a point are equal in lengthDThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)
6$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle BCD $= 116^\circ$. Work out the size of angle DAB, marked $x$.
A90B244C64D116
7In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 110^\circ$. Work out the size of angle $x$.
A70B110C55D35
8$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TOP = 37^\circ$. Work out the size of angle $x$.
A53B90C143D37
9$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CAB $= 44^\circ$. Work out the size of angle CBA, marked $x$.
A90B44C136D46
10$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle CDA $= 80^\circ$. Work out the size of angle ABC, marked $x$.
A90B100C280D80
11In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. Angle $ACB = 50^\circ$. Work out the size of angle $x$.
A100B140C50D130
12In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle between the tangent and the chord $TA$ is $48^\circ$. Work out the size of angle $ABT$ in the alternate segment, marked $x$.
A90B132C96D48
13From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 40^\circ$. Work out the size of angle $PAB$, marked $x$.
A70B140C90D40
14$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 39^\circ$. Work out the size of the angle $AOB$ at the centre.
A141B39C78D102
15$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 37^\circ$. Work out the size of the angle $AOB$ at the centre.
A143B106C37D74
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Circle Theorems · MCQ assessment
Version D
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
/ 15
1$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 51^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in the same segment are equalBThe angle at the centre is twice the angle at the circumferenceCA tangent meets a radius at 90°DOpposite angles of a cyclic quadrilateral add up to 180°
2$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 57^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AOpposite angles of a cyclic quadrilateral add up to 180°BThe angle at the centre is twice the angle at the circumferenceCThe angle in a semicircle is 90°DBase angles of an isosceles triangle are equal
3In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 94^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe angle in a semicircle is 90°BBase angles of an isosceles triangle are equalCAngles in the same segment are equalDThe angle at the centre is twice the angle at the circumference
4From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 66^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AA tangent meets a radius at 90°BThe two tangents from a point are equal in lengthCBase angles of an isosceles triangle are equalDThe angle in a semicircle is 90°
5$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle BCD $= 111^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AOpposite angles of a cyclic quadrilateral add up to 180°BAngles in a triangle add up to 180°CThe angle at the centre is twice the angle at the circumferenceDAngles in the same segment are equal
6In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 84^\circ$. Work out the size of angle $x$.
A96B42C48D84
7$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CAB $= 39^\circ$. Work out the size of angle CBA, marked $x$.
A39B141C51D90
8$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TPO = 60^\circ$. Work out the size of angle $x$.
A90B60C30D120
9$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle DAB $= 84^\circ$. Work out the size of angle BCD, marked $x$.
A96B84C276D90
10In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 114^\circ$. Work out the size of angle $x$.
A66B114C57D33
11$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CAB $= 36^\circ$. Work out the size of angle CBA, marked $x$.
A90B54C36D144
12From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 52^\circ$. Work out the size of angle $PAB$, marked $x$.
A90B52C64D128
13In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle between the tangent and the chord $TA$ is $55^\circ$. Work out the size of angle $ABT$ in the alternate segment, marked $x$.
A110B90C55D125
14From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 72^\circ$. Work out the size of angle $PAB$, marked $x$.
A72B90C108D54
15$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 48^\circ$. Work out the size of the angle $AOB$ at the centre.
A96B132C84D48
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Circle Theorems · MCQ assessment
Version E
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
/ 15
1$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 70^\circ$. Work out the size of angle $ADB$, marked $x$.
A70B140C90D110
2$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle BCD $= 84^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AOpposite angles of a cyclic quadrilateral add up to 180°BAngles in the same segment are equalCThe angle at the centre is twice the angle at the circumferenceDThe angle in a semicircle is 90°
3$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 38^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AOpposite angles of a cyclic quadrilateral add up to 180°BAngles in the same segment are equalCThe angle at the centre is twice the angle at the circumferenceDBase angles of an isosceles triangle are equal
4From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 50^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AA tangent meets a radius at 90°BThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)CThe two tangents from a point are equal in lengthDBase angles of an isosceles triangle are equal
5In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 108^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in the same segment are equalBThe angle in a semicircle is 90°CA tangent meets a radius at 90°DThe angle at the centre is twice the angle at the circumference
6$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle DAB $= 93^\circ$. Work out the size of angle BCD, marked $x$.
A93B87C267D90
7$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CAB $= 53^\circ$. Work out the size of angle CBA, marked $x$.
A37B90C53D127
8In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. Angle $ACB = 48^\circ$. Work out the size of angle $x$.
A132B96C138D48
9$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TOP = 44^\circ$. Work out the size of angle $x$.
A44B136C46D90
10$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle ABC $= 91^\circ$. Work out the size of angle CDA, marked $x$.
A91B90C89D269
11$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CAB $= 36^\circ$. Work out the size of angle CBA, marked $x$.
A54B90C36D144
12In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle $ABT$ in the alternate segment is $35^\circ$. Work out the size of the angle between the tangent and the chord $TA$, marked $x$.
A90B145C70D35
13From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 48^\circ$. Work out the size of angle $PAB$, marked $x$.
A90B132C66D48
14In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle $ABT$ in the alternate segment is $67^\circ$. Work out the size of the angle between the tangent and the chord $TA$, marked $x$.
A67B113C134D90
15$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 50^\circ$. Work out the size of the angle $AOB$ at the centre.
A80B100C130D50
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Circle Theorems · MCQ assessment
Version F
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
/ 15
1$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 58^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in a triangle add up to 180°BThe angle at the centre is twice the angle at the circumferenceCThe angle in a semicircle is 90°DOpposite angles of a cyclic quadrilateral add up to 180°
2$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 58^\circ$. Work out the size of angle $ADB$, marked $x$.
A58B116C122D90
3$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TOP = 28^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in the same segment are equalBThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)CThe two tangents from a point are equal in lengthDA tangent meets a radius at 90°
4In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle $ABT$ in the alternate segment is $59^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AA tangent meets a radius at 90°BAngles in the same segment are equalCOpposite angles of a cyclic quadrilateral add up to 180°DThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)
5In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. Angle $ACB = 50^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe angle at the centre is twice the angle at the circumferenceBThe angle in a semicircle is 90°CThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)DAngles in the same segment are equal
6$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle BCD $= 105^\circ$. Work out the size of angle DAB, marked $x$.
A105B75C255D90
7$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 28^\circ$. Work out the size of angle CAB, marked $x$.
A62B90C28D152
8$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TOP = 52^\circ$. Work out the size of angle $x$.
A52B128C90D38
9In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 104^\circ$. Work out the size of angle $x$.
A76B52C104D38
10$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle DAB $= 98^\circ$. Work out the size of angle BCD, marked $x$.
A262B82C98D90
11$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 52^\circ$. Work out the size of angle CAB, marked $x$.
A38B128C52D90
12From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 62^\circ$. Work out the size of angle $PAB$, marked $x$.
A90B62C59D118
13In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle between the tangent and the chord $TA$ is $68^\circ$. Work out the size of angle $ABT$ in the alternate segment, marked $x$.
A112B90C136D68
14$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 66^\circ$. Work out the size of the angle $AOB$ at the centre.
A48B114C66D132
15$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 65^\circ$. Work out the size of the angle $AOB$ at the centre.
A50B130C115D65
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Circle Theorems · MCQ assessment
Version G
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
/ 15
1In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 110^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe angle in a semicircle is 90°BOpposite angles of a cyclic quadrilateral add up to 180°CThe angle at the centre is twice the angle at the circumferenceDAngles in the same segment are equal
2In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle between the tangent and the chord $TA$ is $65^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AA tangent meets a radius at 90°BThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)CThe two tangents from a point are equal in lengthDAngles in the same segment are equal
3$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle DAB $= 69^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in the same segment are equalBOpposite angles of a cyclic quadrilateral add up to 180°CThe angle at the centre is twice the angle at the circumferenceDThe two tangents from a point are equal in length
4From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 64^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe two tangents from a point are equal in lengthBBase angles of an isosceles triangle are equalCA tangent meets a radius at 90°DThe angle at the centre is twice the angle at the circumference
5$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 39^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in the same segment are equalBOpposite angles of a cyclic quadrilateral add up to 180°CThe two tangents from a point are equal in lengthDThe angle at the centre is twice the angle at the circumference
6In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 114^\circ$. Work out the size of angle $x$.
A66B57C114D33
7$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CAB $= 30^\circ$. Work out the size of angle CBA, marked $x$.
A30B90C150D60
8$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TOP = 32^\circ$. Work out the size of angle $x$.
A148B90C58D32
9$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle CDA $= 91^\circ$. Work out the size of angle ABC, marked $x$.
A269B91C90D89
10In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 128^\circ$. Work out the size of angle $x$.
A52B128C64D26
11$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 48^\circ$. Work out the size of angle CAB, marked $x$.
A90B48C132D42
12From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 44^\circ$. Work out the size of angle $PAB$, marked $x$.
A90B136C44D68
13In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle between the tangent and the chord $TA$ is $55^\circ$. Work out the size of angle $ABT$ in the alternate segment, marked $x$.
A110B55C90D125
14From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 64^\circ$. Work out the size of angle $PAB$, marked $x$.
A116B64C90D58
15$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 53^\circ$. Work out the size of the angle $AOB$ at the centre.
A53B74C127D106
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Circle Theorems · MCQ assessment
Version H
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
/ 15
1$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TOP = 48^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AA tangent meets a radius at 90°BThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)CThe two tangents from a point are equal in lengthDThe angle in a semicircle is 90°
2$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 39^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe angle at the centre is twice the angle at the circumferenceBThe angle in a semicircle is 90°COpposite angles of a cyclic quadrilateral add up to 180°DThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)
3In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. Angle $ACB = 56^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe two tangents from a point are equal in lengthBThe angle at the centre is twice the angle at the circumferenceCThe angle in a semicircle is 90°DAngles in the same segment are equal
4$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 67^\circ$. Work out the size of angle $ADB$, marked $x$.
A113B67C134D90
5In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle $ABT$ in the alternate segment is $59^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)BOpposite angles of a cyclic quadrilateral add up to 180°CA tangent meets a radius at 90°DAngles in the same segment are equal
6$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CAB $= 32^\circ$. Work out the size of angle CBA, marked $x$.
A32B58C148D90
7$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TPO = 47^\circ$. Work out the size of angle $x$.
A43B90C133D47
8In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. Angle $ACB = 56^\circ$. Work out the size of angle $x$.
A124B146C56D112
9$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle BCD $= 94^\circ$. Work out the size of angle DAB, marked $x$.
A90B94C266D86
10$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 52^\circ$. Work out the size of angle CAB, marked $x$.
A38B90C52D128
11$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TPO = 52^\circ$. Work out the size of angle $x$.
A38B128C90D52
12From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 36^\circ$. Work out the size of angle $PAB$, marked $x$.
A72B144C90D36
13In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle $ABT$ in the alternate segment is $62^\circ$. Work out the size of the angle between the tangent and the chord $TA$, marked $x$.
A124B90C62D118
14From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 56^\circ$. Work out the size of angle $PAB$, marked $x$.
A90B56C62D124
15$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 55^\circ$. Work out the size of the angle $AOB$ at the centre.
A125B70C110D55
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Circle Theorems · MCQ assessment
Version I
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
/ 15
1$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 69^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AOpposite angles of a cyclic quadrilateral add up to 180°BThe two tangents from a point are equal in lengthCThe angle at the centre is twice the angle at the circumferenceDAngles in the same segment are equal
2$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 61^\circ$. Work out the size of angle $ADB$, marked $x$.
A61B122C90D119
3$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle CDA $= 113^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AOpposite angles of a cyclic quadrilateral add up to 180°BThe angle at the centre is twice the angle at the circumferenceCThe angle in a semicircle is 90°DAngles in the same segment are equal
4$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TPO = 37^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe two tangents from a point are equal in lengthBAngles in the same segment are equalCThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)DA tangent meets a radius at 90°
5$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CAB $= 56^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe angle in a semicircle is 90°BOpposite angles of a cyclic quadrilateral add up to 180°CThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)DThe angle at the centre is twice the angle at the circumference
6$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle ABC $= 67^\circ$. Work out the size of angle CDA, marked $x$.
A90B293C67D113
7In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. Angle $ACB = 63^\circ$. Work out the size of angle $x$.
A117B126C153D63
8$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 36^\circ$. Work out the size of angle CAB, marked $x$.
A36B54C144D90
9$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TPO = 51^\circ$. Work out the size of angle $x$.
A129B51C90D39
10$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle DAB $= 84^\circ$. Work out the size of angle BCD, marked $x$.
A96B90C84D276
11In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. Angle $ACB = 52^\circ$. Work out the size of angle $x$.
A142B52C104D128
12In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle between the tangent and the chord $TA$ is $55^\circ$. Work out the size of angle $ABT$ in the alternate segment, marked $x$.
A110B90C55D125
13From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 56^\circ$. Work out the size of angle $PAB$, marked $x$.
A90B124C62D56
14In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle $ABT$ in the alternate segment is $69^\circ$. Work out the size of the angle between the tangent and the chord $TA$, marked $x$.
A111B138C90D69
15$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 66^\circ$. Work out the size of the angle $AOB$ at the centre.
A66B114C48D132
How confident do you feel on this topic now?RedAmberGreen
Circle Theorems · MCQ assessment
Version J
Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______
Mark bar · shade a box for each question you got right
123456789101112131415
/ 15
1$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TPO = 61^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
ABase angles of an isosceles triangle are equalBThe two tangents from a point are equal in lengthCA tangent meets a radius at 90°DThe alternate segment theorem (tangent–chord angle equals the angle in the alternate segment)
2$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 50^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AThe angle in a semicircle is 90°BBase angles of an isosceles triangle are equalCOpposite angles of a cyclic quadrilateral add up to 180°DThe angle at the centre is twice the angle at the circumference
3$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle CDA $= 76^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AOpposite angles of a cyclic quadrilateral add up to 180°BThe angle at the centre is twice the angle at the circumferenceCAngles in the same segment are equalDThe angle in a semicircle is 90°
4$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 30^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
AAngles in the same segment are equalBThe angle in a semicircle is 90°COpposite angles of a cyclic quadrilateral add up to 180°DThe angle at the centre is twice the angle at the circumference
5From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 62^\circ$. Which circle theorem did you use to find $x$? Give a reason for your answer.
ABase angles of an isosceles triangle are equalBA tangent meets a radius at 90°CThe angle in a semicircle is 90°DThe two tangents from a point are equal in length
6$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle BCD $= 101^\circ$. Work out the size of angle DAB, marked $x$.
A101B90C259D79
7$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TOP = 61^\circ$. Work out the size of angle $x$.
A119B29C61D90
8$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 40^\circ$. Work out the size of angle CAB, marked $x$.
A90B50C140D40
9In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 86^\circ$. Work out the size of angle $x$.
A86B47C94D43
10$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle ABC $= 80^\circ$. Work out the size of angle CDA, marked $x$.
A80B280C100D90
11$T$ is a point on a circle, centre $O$. $TP$ is a tangent to the circle. Angle $TPO = 38^\circ$. Work out the size of angle $x$.
A142B52C90D38
12From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 48^\circ$. Work out the size of angle $PAB$, marked $x$.
A48B90C132D66
13In the diagram, $T$ is a point on a circle and the straight line through $T$ is a tangent. $TA$ is a chord and $B$ is a point on the circle. The angle $ABT$ in the alternate segment is $56^\circ$. Work out the size of the angle between the tangent and the chord $TA$, marked $x$.
A90B124C112D56
14From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 78^\circ$. Work out the size of angle $PAB$, marked $x$.
A90B78C102D51
15$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 56^\circ$. Work out the size of the angle $AOB$ at the centre.
A68B124C56D112
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