Circle Theorems Worksheet

A Grade 11 Math worksheet covering various circle theorems including tangent-chord theorem, angles in a cyclic quadrilateral, and angles subtended by an arc.

Grade 11 Math GeometryCircle Theorems

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Includes

3 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSG.C.A.3CCSS.MATH.CONTENT.HSG.C.A.2

Topics

MathGeometryCircle TheoremsGrade 11

8 sections · Free to use · Printable

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Circle Theorems Worksheet

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Read each question carefully and answer to the best of your ability. Show all your workings for full credit.

1. In the diagram below, AB is a tangent to the circle at point C. CD is a chord. If ∠BCD = 70°, find the measure of ∠CAD.

2. Which of the following statements is true for a cyclic quadrilateral?

Opposite angles are equal.

Adjacent angles sum to 180°.

Opposite angles sum to 180°.

All angles are equal.

3. The angle subtended by an arc at the center of a circle is the angle subtended by the same arc at any point on the remaining part of the circle.

4. Points A, B, C, and D lie on a circle. If ∠ACB = 40° and ∠DBC = 30°, find ∠ADB.

5. A tangent to a circle is always perpendicular to the radius at the point of tangency.

True

False

6. In the diagram, PQ is a tangent to the circle at R. S is a point on the circle such that RS is a chord. T is another point on the circle. If ∠QRT = 65°, find ∠RST.