CAIE IGCSE Mathematics Core C4.7 Circle Theorems Topic Practice

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Covered syllabus points

C4.7.1 Calculate unknown angles and give explanations using the following

Question 1

[Maximum number: 1]
Figure for Question 1 — CAIE IGCSE Mathematics Core

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∘90^{\circ}.

Question 2

[Maximum number: 2]
NOT TO SCALE

NOT TO SCALE

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

Question 3

[Maximum number: 2]
NOT TO SCALE

NOT TO SCALE

A, B and C lie on the circumference of the circle, centre O. AB is a diameter.
DBE is a tangent to the circle at B.
Find the value of x.
Give a geometrical reason for your answer. because

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