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.
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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.
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