Question

In figure, if O is the centre of a circle PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal to ______.

 

Options

• 100°

• 80°

• 90°

• 75°

Answer 1

In figure, if O is the centre of a circle PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal to 100°.

Explanation:

OP ⊥ PR  ...[Tangent and radius are ⊥ to each other at the point of contact]

∠OPQ = 90° – 50° = 40°

OP = OQ  ...[Radii]

∴ ∠OPQ = ∠OQP = 40°

In ∆OPQ,

⇒ ∠POQ + ∠OPQ + ∠OQP = 180°

⇒ ∠POQ + 40° + 40° = 180°

∠POQ = 180° – 80° = 100°.