Question

In Figure, O is the centre of circle. PQ is a chord and PT is tangent at P which makes an angle of 50° with PQ. ∠POQ is

Options

• 130°

• 90°

• 100°

• 75°

Answer 1

100°

Explanation:

Since, ∠OPT = 90°   ...[Angle between radius and tangent]

∴ ∠OPQ = 90° – 50° = 40°

Also, OP = OQ   ...[Radii of a circle]

⇒ ∠OPQ = ∠OQP = 40°   ...[Equal opposite sides have equal opposite angles]

∴ ∠POQ = 180° – ∠OPQ – ∠OQP   ...[Angle sum properly of a triangle]

= 180° – 40° – 40°

= 100°