Question

If PA and PB are two tangents to a circle with centre O such that ∠AOB = 110° then ∠APB is equal to ______.

पर्याय

• 55°

• 60°

• 70°

• 90°

Answer 1

If PA and PB are two tangents to a circle with centre O such that ∠AOB = 110° then ∠APB is equal to 70°.

Explanation:

OA and OB are radii to the tangent points, so OA ⟂ PA and OB ⟂ PB.

In quadrilateral APBO the angles are ∠OAP = 90°, ∠AOB = 110°, ∠OBP = 90° and ∠APB = x.

Sum = 360°, so x + 90 + 110 + 90 = 360 ⇒ x = 70°.