Question 49
Circle TheoremsIn the figure above, PT is a tangent to the circle with centre at O. If PQT = 30°, find the value of PTO.
- A.30°
- B.15°
- C.24°
- D.12°
- E.60°.
Show the answer and explanation
Answer: A (30°)
Explanation
OP ⊥ PT, and triangle OPQ is isosceles, so <QPT = 90° + x. In triangle PQT: 30° + (90° + x) + 3x = 180°, giving x = 15°. So <PTO = 2x = 30°.