1

$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 48^\circ$. Work out the size of angle $ADB$, marked $x$. [2]

2

$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 27^\circ$. Work out the size of angle $ADB$, marked $x$. [2]

3

$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 34^\circ$. Work out the size of angle $ADB$, marked $x$. [2]

4

$A$, $B$, $C$ and $D$ are points on a circle. Angle $ACB = 25^\circ$. Work out the size of angle $ADB$, marked $x$. [2]

5

In the diagram, $A$, $B$ and $C$ are points on a circle, centre $O$. The angle at the centre $AOB = 74^\circ$. Work out the size of angle $x$. [2]

6

$A$, $B$ and $C$ are points on a circle and $AB$ is a diameter. Angle CBA $= 60^\circ$. Work out the size of angle CAB, marked $x$. [2]

7

$A$, $B$, $C$ and $D$ are points on a circle, forming a cyclic quadrilateral $ABCD$. Angle CDA $= 88^\circ$. Work out the size of angle ABC, marked $x$. [2]

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 $x$. [2]

9

$A$, $B$ and $C$ are points on a circle, centre $O$. $OA$ and $OB$ are radii. Angle $OAB = 54^\circ$. Work out the size of the angle $AOB$ at the centre. [1]

10

From a point $P$ outside a circle, centre $O$, two tangents are drawn touching the circle at $A$ and $B$. Angle $APB = 66^\circ$. Work out the size of angle $PAB$, marked $x$. [2]

11

In 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 $44^\circ$. Work out the size of the angle between the tangent and the chord $TA$, marked $x$. [2]