Question

In the given figure, O is the centre of a circle and PT is the tangent to the circle. If PQ is a chord such that ∠QPT = 50° then ∠POQ = ?

Options

• 100°

• 90°

• 80°

• 75°

Answer 1

100°

Explanation:

Mark a point R in the alternate segment.

Join PR and QR.

Then, ∠PRQ = ∠QPT = 50°   ...[Angles in alternate segments]

Now, ∠POQ = 2∠PRQ = 100°   ...[∵ Angle at the centre is double the angle on the circle]