Question

In the given figure, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70° then ∠TPQ is equal to ______.

Options

• 35°

• 45°

• 55°

• 70°

Answer 1

In the given figure, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70° then ∠TPQ is equal to 35°.

Explanation:

Mark a point R in the alternate segment.

Join PR and QR.

Then, `∠PRQ = 1/2 ∠POQ = 1/2 xx 70^circ = 35^circ`.

Now, ∠TPQ = ∠PRQ = 35°   ...[Angles in alternate segments]