Question 22
Circle TheoremsIn the diagram, the tangent MN makes an angle of 55° with chord PS. If O is the centre of the circle, find ∠RPS.
- A.55°
- B.45°
- C.35°
- D.25°
Show the answer and explanation
Answer: C (35°)
Explanation
By the alternate segment theorem, ∠PRS = 55°. PR is a diameter, so ∠PSR = 90°. Then ∠RPS = 180° − 90° − 55° = 35°.