Mastering Circle Theorems
Mathematics
GCSE Foundation
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A worksheet covering Circle Theorems for GCSE Foundation students.
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Mastering Circle Theorems
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Review the key circle theorems: the angles subtended by the same arc are equal, angles in a semicircle are right angles, and the angle between a tangent and a chord equals the angle in the alternate segment.
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
In a circle with centre O, chord AB is 8 cm long. The distance from O to AB is 3 cm. Calculate the radius of the circle.
[3 marks]2.
Angles A and B are inscribed in a circle and subtend the same arc. If angle A is 40°, what is the measure of angle B?
[2 marks]3.
In the diagram, a tangent at point P touches the circle at P. The angle between the tangent and chord PQ is 60°. Find the measure of angle QPR in the same segment.
[2 marks]4.
Calculate the measure of the angle between two radii of a circle that subtend a 120° arc at the circumference.
[2 marks]5.
In a circle, an inscribed triangle has angles 50°, 60°, and x°. Find the value of x°.
[2 marks]6.
A diameter of a circle subtends a right angle at any point on the circle. Explain why this is true using circle theorems.
[3 marks]7.
Identify and explain the theorem used when two angles in the same segment of a circle are equal.
[3 marks]8.
In the diagram, a tangent and a radius form a 90° angle at the point of contact. If the tangent is extended to meet a chord at an angle of 70°, find the measure of the angle between the radius and the chord.
[2 marks]9.
A cyclic quadrilateral has angles 110°, 70°, and two unknown angles. Find the measures of the unknown angles.
[3 marks]10.
A real-world scenario: A circular fountain has a diameter of 10 meters. A sculpture is placed 3 meters from the centre along a radius. Calculate the distance from the sculpture to a point on the circumference directly opposite the sculpture along the diameter.
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- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
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