Question

If O is centre of a circle and Chord PQ makes an angle 50° with the tangent PR at the point of contact P, then the angle subtended by the chord at the centre is ______.

पर्याय

• 130°

• 100°

• 50°

• 30°

Answer 1

If O is centre of a circle and Chord PQ makes an angle 50° with the tangent PR at the point of contact P, then the angle subtended by the chord at the centre is 100°.

Explanation:

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

∠OPQ = 90° – 50° = 40°

OP = OQ   ...[Radii]

∴ ∠OPQ = ∠OQP = 40°

In ΔOPQ,

`\implies` ∠POQ + ∠OPQ + ∠OQP = 180°

`\implies` ∠POQ + 40° + 40° = 180°

∠POQ = 180° – 80° = 100°.