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JAMB Mathematics 1995 Question 27

Question 27

Circle Theorems

PT is a tangent to the circle TYZX, YT = YX and ∠PTX = 50°. Calculate ∠TZY

Diagram for this question
  1. A.50°
  2. B.65°
  3. C.85°
  4. D.130°
Show the answer and explanation

Answer: B (65°)

Explanation

By the alternate segment theorem, angle XYT = angle PTX = 50°. Triangle XYT is isosceles (YT = YX), so angle TXY = (180° − 50°)/2 = 65°. Angle TZY stands on the same arc TY, so it is also 65°.