In the given figure, O is the centre of a circle and ∠AOC = 120°. Then, ∠BDC = ?

Question

In the given figure, O is the centre of a circle and ∠ AOC = 120°. Then, ∠ BDC = ?

Philoid · Accepted Answer

Given: ∠AOC = 120°

Construction: Join OD

We know that,

∠AOC = 2 × ∠ADC

120° = 2 ∠ADC

∠ADC = 60°

Here,

∠ADB = 90° (angle in a semicircle)

∠ADB = ∠ADC + ∠CDB = 90°

∠ADC + ∠CDB = 90°

60° + ∠CDB = 90°

∠CDB = 90° – 60°

∠CDB = 30°

∴ ∠BDC = 30°