CAIE IGCSE Mathematics Core C4.7 Circle Theorems Topic Practice

The diagram shows a circle, centre O, radius 11 cm. C, F, G and H are points on the circumference of the circle.
The line AD touches the circle at C and is parallel to the line EG. B is a point on AD and angle $A B O=140^{\circ}$.

Give a reason why angle BCO is $90^{\circ}$.

The diagram shows a circle, centre O, with diameter PQ. R is a point on the circumference.

Give a geometrical reason why angle PRQ is $90^{\circ}$.

The diagram shows a circle, centre O, diameter AB. A, B and C lie on the circumference of the circle.

Find the value of x.
Give a geometrical reason for your answer.
x=
because