Question

In the given figure, tangents PA and PB drawn from P to circle are inclined to each other at an angle of 80°. The measure of ∠PAB is ______.

पर्याय

• 80°

• 60°

• 50°

• 40°

Answer 1

In the given figure, tangents PA and PB drawn from P to circle are inclined to each other at an angle of 80°. The measure of ∠PAB is 50°.

Explanation:

We know that the lengths of tangents drawn from an external point to a circle are equal.

i.e. AP = BP  ...[length of the tangents]

∴ ∠PBA = ∠PAB  ...(i) [∵ angles opposite to equal sides of a triangle are equal]

In ΔPAB, we have

∴ ∠PAB + ∠PBA + ∠APB = 180°  ...[by angle sum property]

∴ ∠PAB + ∠PAB + 80° = 180°  ...[using Eq. (i) and ∠APB = 80°]

∴ 2∠PAB = 100°

∴ ∠PAB = 50°

Hence, the measure of ∠PAB is 50°.