Mastering Circle Theorems
Mathematics
GCSE Higher
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A worksheet covering Circle Theorems for GCSE Higher students.
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Mastering Circle Theorems
Subject: MathematicsGrade: GCSE Higher
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Date:
Untitled Worksheet
Grade GCSE Higher
A
Introduction
Study the key concepts of circle theorems below before attempting the questions.
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
In a circle, angle subtended at the center by a diameter is 180°. True or False?
[1 mark]2.
Calculate the size of the angle subtended at the circumference by a chord that subtends a 60° angle at the center.
[2 marks]3.
In a cyclic quadrilateral, opposite angles are supplementary. Explain why this must be true.
[3 marks]4.
A chord in a circle subtends a 45° angle at the center. What is the measure of the inscribed angle subtended by the same chord?
[2 marks]5.
Identify which of the following angles are inscribed angles in the circle:
(a) 70° at the circumference
(b) 140° at the circumference
(c) 50° at the center
[1 mark]6.
A cyclic quadrilateral ABCD has angles at A and C equal to 110° and 70° respectively. Find angles at B and D.
[3 marks]7.
Prove that the angle between a tangent and a chord at the point of contact is equal to the inscribed angle subtended by the chord.
[3 marks]8.
If a radius of a circle is 10 cm, and an inscribed angle subtends an arc of 60°, find the length of the arc.
[3 marks]9.
A chord AB subtends a 70° angle at the center of the circle. What is the measure of the inscribed angle subtended by the same chord?
[2 marks]10.
In real-world applications, explain how circle theorems can be used in designing gears or circular tracks.
[3 marks]Quick Actions
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- Created
- 12/30/2025
- Updated
- 12/30/2025
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