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JAMB Mathematics 1998 Question 28

Question 28

Circle Theorems

TQ is tangent to a circle XYTR, ∠YXT = 32°, ∠RTQ = 40°. Find ∠YTR

Diagram for this question
  1. A.108°
  2. B.121°
  3. C.140°
  4. D.148°
Show the answer and explanation

Answer: A (108°)

Explanation

By the alternate segment theorem ∠RXT = ∠RTQ = 40°, so ∠YXR = 32° + 40° = 72°. Opposite angles of cyclic quadrilateral XYTR add to 180°, so ∠YTR = 108°.