Question

PA and PB are tangents to a circle with centre O. If ∠AOB = 105°, then ∠OAP + ∠APB is equal to:

विकल्प

• 75°

• 175°

• 180°

• 165°

Answer 1

165°

Explanation:

Given, ∠AOB = 105°

The angle between a tangent and the radius at the point of contact is 90°.

So, ∠OAP = ∠OBP = 90°

We know that the sum of angles in a quadrilateral is 360°.

∴ ∠AOB + ∠OAP + ∠OBP + ∠APB = 360°

⇒ 105° + ∠OАР + 90° + ∠APB = 360°

⇒ ∠OAP + ∠APB + 195° = 360°

⇒ ∠OAP + ∠APB = 360° – 195°

⇒ ∠OAP + ∠APB = 165°