IGCSE Math B 6.K Circle theorems Topic Practice

The diagram shows a circle JKLM.
JKP and LMP are straight lines.
$$JK=3\text{ cm},\qquad KP=2.5\text{ cm},\qquad PM=2\text{ cm}.$$$$\angle JPL=74^\circ.$$
Calculate the area, in $\text{cm}^2$ to 2 decimal places, of triangle LKP.

A, B, C and D are points on a circle, centre O.
Angle $A D C=132^{\circ}$
Calculate, in degrees, the size of angle x.

Diagram NOT accurately drawn

Figure 1 shows the circle ABCD with centre O and diameter DC. The point T is such that TCOD is a straight line and TA is the tangent to the circle at A.

Calculate the radius, in cm , of the circle.

Diagram NOT accurately drawn
A, C, B and D are four points on a circle.
The chord AB intersects the chord CD at P.

Calculate, in cm, the length of CP.

In the diagram, A, B, C and D are four points on the circle ABCD.
The point P lies outside the circle ABCD so that BCP and ADP are straight lines. $C P=10 \mathrm{~cm}, A D=12 \mathrm{~cm}$ and $D P=8 \mathrm{~cm}$.

Calculate the length, in cm, of BC.

In the diagram, A, B and C are three points on the circle ABC.
AE is the tangent to the circle at the point A.
DCE is the tangent to the circle at the point C.
RBD is the tangent to the circle at the point B.
$\angle C A E=60^{\circ}$ and $\angle C B R=135^{\circ}$
Giving your reasons, find the size in degrees of $\angle A C B$.

A, B and C are three points on a circle, with centre O, as shown in the diagram.
BC is a diameter of the circle.
The point D is such that BOCD is a straight line and AD is the tangent to the circle at A. $A D=5 \mathrm{~cm}$ and $C D=4 \mathrm{~cm}$.

Calculate the radius, in cm, of the circle.

Diagram NOT accurately drawn.

In the diagram A, B, C and D are points on a circle.
AEC is a diameter of the circle.
BED is a chord of the circle.
$AE=5\text{ cm}$, $BE=7\text{ cm}$ and $ED=13\text{ cm}$.
Calculate, in cm, the radius of the circle.

Diagram NOT accurately drawn.

P, Q and R are three points on a circle, centre O.
$\angle POR=124^\circ$.
Calculate the size, in degrees, of $\angle PQR$.
Give reasons for each stage of your working.

The diagram shows a circle ABCD where the line PAQ is the tangent to the circle at A.

Giving your reasons, find, in degrees, the size of $\angle B A C$.