In the given figure, O is the centre of a circle, BC is a diameter and ∠BAO = 60°. Then, ∠ADC = ?

Question

In the given figure, O is the centre of a circle, BC is a diameter and ∠ BAO = 60°. Then, ∠ ADC = ?

Philoid · Accepted Answer

Given:

Consider ΔAOB

Here,

OA = OB (radius)

∠OBA = ∠OAB = 60° (angles opposite to equal sides are equal)

By angle sum property

∠OBA + ∠OAB + ∠AOB = 180°

60° + 60° + ∠AOB = 180°

∠AOB = 180° — 60° — 60° = 60°

Here,

∠BOC = ∠BOA + ∠AOC = 180°

60° + ∠AOC = 180°

∠AOC = 180° – 60° = 120°

We know that,

∠AOC = 2× ∠ADC

∠AOC = ∠ADC

×120° = ∠ADC

∠ADC = 60°

∴∠ADC = 60°