In Figure, O is the centre of the circle. If ∠APB . . .

Question : In Figure, O is the centre of the circle. If ∠APB=50°, find ∠AOB and ∠OAB. [RD Sharma]

Doubt by Aditi

Solution : 

We know, 
∠AOB = 2∠APB [Angle subtended by an arc at the centre is twice the angle subtended by it at any point on the remaining part of the circle]

∠AOB = 2×50°

∠AOB = 100°

Join AB

In ΔAOB

OA=OB (Radii of the same circle)
∠OAB=∠OBA (Angles opposite to equal sides of a triangle are equal)

∠OAB+∠AOB+∠OBA=180° (ASP)

∠OAB+∠AOB+∠OAB=180° (∵∠OAB=∠OBA)
2∠OAB+100°=180°
2∠OAB=180°-100°
2∠OAB=80°
∠OAB=80°/2
∠OAB=40°

Hence, ∠AOB=100° & ∠OAB=40°