Question

In the given figure, O is the centre of a circle, PQ is a chord and the tangent PT at P makes an angle of 50° with PQ. Then, ∠POQ = ?

Options

• 130°

• 100°

• 90°

• 75°

Answer 1

100°

Explanation:

By the tangent–chord (alternate-segment) theorem, the angle between the tangent PT and chord PQ equals the angle subtended by chord PQ at the circumference so that inscribed angle = 50°. The central angle subtending the same chord is twice the inscribed angle, so ∠POQ = 2 × 50° = 100°.