Mastering Circle Theorems

Mathematics
Year 9
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A worksheet covering Circle Theorems for Year 9 students.

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Mastering Circle Theorems

Subject: MathematicsGrade: Year 9
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Date:

Untitled Worksheet

Grade Year 9
A

Introduction

Review the key circle theorems: the angles subtended by the same arc are equal, the angle at the centre is twice the angle at the circumference, and the opposite angles of a cyclic quadrilateral sum to 180°. Use these to solve the following questions.
B

Practice Questions

Answer all questions. Show your working in the grid spaces provided.
1.
In a circle, an inscribed angle subtends an arc of 80°. What is the measure of the angle at the circumference subtending the same arc?
[2 marks]
2.
Calculate the angle at the centre of a circle if the inscribed angle subtending the same arc measures 30°.
[2 marks]
3.
In a cyclic quadrilateral, three angles measure 70°, 80°, and 60°. What is the measure of the fourth angle?
[3 marks]
4.
Two points on a circle subtend a 50° angle at the circumference. What is the measure of the arc between these two points?
[2 marks]
5.
A diameter of a circle subtends an inscribed angle of 30°. What is the measure of the other inscribed angles subtending the same arc?
[2 marks]
6.
In a circle, an angle at the centre is 120°. Find the measure of the inscribed angle subtending the same arc.
[2 marks]
7.
Prove that the opposite angles of a cyclic quadrilateral are supplementary.
[4 marks]
8.
In a circle, two chords intersect inside the circle. The angle formed between the chords is 40°. Find the measure of the angles at the intersection point formed by the two chords.
[3 marks]
9.
A circle has a radius of 10 cm. Calculate the length of an arc subtending a 60° angle at the centre.
[3 marks]
10.
A real-world application: A circular fountain has a diameter of 12 meters. If a person stands at a point on the circumference, what is the measure of the angle at the centre between two points on the circumference that subtend a 90° angle at the person's position?
[4 marks]

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Details

Created
12/30/2025
Updated
12/30/2025
Type
worksheet