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WAEC Mathematics 1991 (August) Question 29

Question 29

Circle Theorems

In the diagram above, ATR is a tangent at the point T; to the circle centre O, if ∠TOB = 145°, find ∠TAO

Diagram for this question
  1. A.20°
  2. B.35°
  3. C.45°
  4. D.55°
  5. E.65°
Show the answer and explanation

Answer: D (55°)

Explanation

AOB is a straight line, so ∠AOT = 180° − 145° = 35°. The radius OT is perpendicular to the tangent, so ∠TAO = 180° − 90° − 35° = 55°.