Question

In the given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 50° then what is the measure of ∠OAB.

Answer 1

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° + 50° + 90° = 360°
⇒ 230° + ∠BOC= 360°

⇒ ∠AOB = 130°
Now, In isosceles triangle AOB
∠AOB  + ∠OAB  +∠OBA =180°       [Angle sum property of a triangle]
⇒ 130° + 2∠OAB = 180°          [∵ ∠OAB =  ∠OAB]
⇒ ∠OAB = 25°