Question

In fig, AB is a chord of a circle with center O. If ∠ACD = 40°, then find ∠OAB.

Answer 1

We know that angle subtended by arc at the center of circle is double the angle subtended at remaining part of circle.

∠AOB = 2∠ACB

∠AOB = 2 × 40° [∵ ∠ACB = 40°]

∠AOB = 80°

OA = OB (Radius of circle)

∴ ∠OAB = ∠OBA

In ΔOAB

∠OAB + ∠OBA + ∠AOB = 180°

∠OAB + ∠OAB + 90° = 180°

2∠OAB = 180° – 90°

2∠OAB = 90°

∠OAB = \(\frac { { 90 }^{ \circ } }{ 2 } \)

Thus, ∠OAB = 45°.