Grade 11 Circle Proofs Worksheet
A worksheet for Grade 11 students to practice and demonstrate their understanding of circle theorems and proofs.
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Grade 11 Circle Proofs Worksheet
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Read each question carefully and provide clear, logical proofs or answers. Show all your work.
1. Prove that the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
2. In a cyclic quadrilateral, the sum of opposite angles is degrees.
3. The angle in a semicircle is a angle.
4. A tangent to a circle is perpendicular to the radius at the point of tangency.
True
False
5. Which of the following is true about chords equidistant from the center of a circle?
They are parallel.
They are equal in length.
They bisect each other.
They are perpendicular.
6. In the circle below, O is the center. If ∠AOB = 80°, find ∠ACB. Provide a reason for your answer.
7. Prove that a line drawn from the center of a circle to bisect a chord is perpendicular to the chord.