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Circle Theorems Worksheet

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Circle Theorems Worksheet

Solve each circle-theorem challenge. Show your calculations and include the theorem you used where asked. Angles are in degrees.

The Observatory Challenge

A team is checking the geometry of a circular observation platform. Use the given information and circle theorems to help them.

1.∠AOB = 96°. Find ∠ACB, which stands on the same minor arc AB. Explain the theorem you used.

2.A second point D lies on the same segment of the circle as C, and ∠ADB also stands on chord AB. What is ∠ADB?

Angles Around the Platform

The platform boundary forms a cyclic quadrilateral. Opposite vertices lie on the circle.

3.In cyclic quadrilateral PQRS, ∠P = 73° and ∠Q = 118°. Find ∠R and ∠S. State the property used.

4.At a maintenance point outside the circle, two straight lines touch the platform at X and Y. If the tangent length from the point to X is 8.4 m, what is the tangent length to Y?

4.2 m
8.4 m
16.8 m
It cannot be determined

Tangent Tests

The surveyors check a tangent and a chord at the edge of the circle.

5.The radius OT meets the tangent at T. What is the angle between OT and the tangent?

38°
52°
90°
142°

6.The angle between the tangent and chord TA is 38°. Find the angle in the alternate segment subtended by chord TA. Name the theorem.

Decode the Survey Notes

Use the circle theorems to solve the final checks and explain your reasoning.

7.Two angles in the same segment are labelled (4x + 7)° and (6x − 19)°. Find x, then calculate the size of each angle.

8.A chord AB subtends an angle of 34° at the circumference. What is the smaller angle at the centre standing on the same arc AB?

9.A colleague claims, “The angle between any chord and a tangent is always 90°.” Is this correct? Correct the claim using the 38° tangent–chord angle stated above and a circle theorem.

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More Maths Worksheets

Circle Theorems Worksheet

Circle Theorems Worksheet

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Angles Around the Platform

Tangent Tests

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2 printable pages

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

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