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WAEC Mathematics 1999 Question 18

Question 18

Circle Theorems

In the diagram, RST is a tangent to circle VSU centre O. ∠SVU = 50° and UV is a diameter. Calculate ∠RSV

Diagram for this question
  1. A.90°
  2. B.50°
  3. C.45°
  4. D.40°.
Show the answer and explanation

Answer: D (40°.)

Explanation

∠VSU = 90° (angle in a semicircle), so ∠SUV = 40°. The angle between tangent and chord, ∠RSV, equals ∠SUV in the alternate segment: 40°.