#### Question

In the given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 60° then find the measure of ∠OAB.

#### Solution

Construction: Join OB

We know that the radius and tangent are perpendicular at their point of contact

∵ ∠OBP = ∠OAP = 90°

Now, In quadrilateral AOBP

∠AOB + ∠OBP + ∠APB +∠OAP = 360° [Angle sum property of a quadrilateral]

⇒ ∠AOB +90° + 60° + 90° = 360°

⇒ 240° + ∠AOB = 360°

⇒ ∠ AOB = 120°

Now, In isosceles triangle AOB

∠AOB + ∠OAB + ∠OBA = 180° [Angle sum property of a triangle]

⇒ 120° + 2 ∠OAB =180° [∵ ∠OAB = ∠OBA]

⇒ ∠OAB = 30°

Is there an error in this question or solution?

Solution In the Given Figure, Pa and Pb Are Two Tangents to the Circle with Centre O. If ∠Apb = 60° Then Find the Measure of ∠Oab. Concept: Circles Examples and Solutions.