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 ?
So,
PA=PB⇒∠PAB=∠PBA...(Angles opposite to equal sides are equal.)Now in triangle PAB, ∠PAB+∠PBA+50°=180°⇒2∠PAB+50°=180°⇒∠PAB=65°
Since AP is a tangent to the circle,
∠OAP=90°⇒∠OAB+∠PAB=90°⇒∠OAB+65°=90°⇒∠OAB=25°