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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Untitled Worksheet
Grade Year 9
A
Introduction
Review the key circle theorems: the angle at the centre is twice the angle at the circumference, angles in a semicircle are right angles, and the angles in the same segment are equal.
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
In a circle, an inscribed angle measures 40°. What is the measure of the arc intercepted by this angle?
[2 marks]2.
Calculate the size of the angle at the centre of a circle if the inscribed angle subtending the same arc measures 35°.
[2 marks]3.
Determine the size of the angle between two radii in a circle with a central angle of 120°.
[2 marks]4.
In a semicircle, what is the measure of the angle where the diameter intersects the circle?
[2 marks]5.
A chord in a circle subtends an inscribed angle of 50°. What is the measure of the intercepted arc?
[2 marks]6.
Two angles in the same segment of a circle measure 45° and 75°. Are these angles correctly positioned? Explain your reasoning.
[3 marks]7.
A circle has a radius of 10 cm. Calculate the length of an arc subtended by a central angle of 60°.
[3 marks]8.
If two angles in a circle are both inscribed and subtend arcs of 80° and 120° respectively, are these angles equal? Justify your answer.
[3 marks]9.
A wheel with radius 15 cm rotates so that a point on its circumference traces an arc of 90°. How far does the point travel along the arc?
[3 marks]10.
Challenge: A park has a circular pond with a diameter of 20 meters. A walkway runs along the edge of the pond. If a person walks halfway around the pond, how far do they walk? Express your answer as a simplified exact value.
[4 marks]11.
Real-world application: A satellite orbits a circular planet at a height of 300 km above the surface. If the radius of the planet is 6371 km, calculate the length of the satellite’s orbit.
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- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet