Question

In the given figure, PA and PB are two tangents to the circle with centre O. If $\angle$ APB = ${50}^o$ then what is the measure of $\angle$ OAB.

Answer 1

∠APB = 50°
∠OAP =∠OBP = 90°
∠OAP +∠OBP=90+90=180°

By angle sum property of quadrilateral, AOBP
∠OAP+∠APB+∠PBO+∠BOA=360°
∠APB+∠AOB =180°
∠AOB = 130°
In△AOB, OA=OB (radii of circle)So,
∠OAB = ∠OBA = x (angles opposite to equal sides are equal)By angle sum property of triangle
in △AOB
x + x + 130 = 180
x =∠OAB= 25 °