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WAEC Mathematics 2004 Question 27

Question 27

Circle Theorems

In the diagram, KS is a tangent to the circle centre O at R and ∠ROQ = 80°. Find ∠QRS.

Diagram for this question
  1. A.90°
  2. B.80°
  3. C.50°
  4. D.40°
Show the answer and explanation

Answer: D (40°)

Explanation

The angle between the tangent and chord RQ equals the angle in the alternate segment, ∠RPQ, which is half the central angle: ½ × 80° = 40°.