passwella.
Menu

GCE Mathematics 1990 Question 37

Question 37

Circle Theorems

In the diagram, PQ is a tangent at T to the circle ABT. ABC is a straight line and TC bisects ∠BTQ. Find x.

Diagram for this question
  1. A.20°
  2. B.30°
  3. C.35°
  4. D.40°
  5. E.50°
Show the answer and explanation

Answer: E (50°)

Explanation

By the alternate segment theorem, ∠BTQ = ∠BAT = 40° and ∠ABT = ∠ATP = 70°. TC bisects ∠BTQ, so ∠BTC = 20°. In triangle BTC the exterior angle ∠ABT = ∠BTC + x, so x = 70° − 20° = 50°.