Question

In the given figure, PT is tangent to a circle with centre O. Chord PQ subtends an angle of 65° at the centre. The measure of ∠QPT is ______. 

Options

• 65°

• 57.5°

• 67.5°

• 32.5°

Answer 1

In the given figure, PT is tangent to a circle with centre O. Chord PQ subtends an angle of 65° at the centre. The measure of ∠QPT is 32.5°.

Explanation:

∠OPQ + ∠OQP + ∠QOP = 180°

2∠OPQ + 65° = 180°

∠OPQ = `(180 - 65)/2`

= 57.5°

∠OPT = 90°

∠OPQ + ∠QPT = 90°

∠QPT = 90° − 57.5°

= 32.5°