Question

In the following 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 the following 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:

From figure using properties of circle and tangents

∠OPQ = 90° - 50°

∠OPQ = 40°

OP = OQ = radius

So (∠E) = ∠OQP = 40°

Now In ∆POQ

∠POQ = 180° – (∠OPQ + ∠OQP)

∠POQ = 180° – (40° + 40°)

∠POQ = 100°