In Fig., A, B, and C are three points on a circle with centre O such t

1.	In Fig., A, B, and C are three points on a circle with centre O such that ∠BOC = 30° and ∠AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.
Answer» ∠AOB + ∠BOC = 60° + 30° = 90° ∴ ∠AOC = 90° (Angle subtended at the centre) ∠ADC = ? The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. ∴ Angle subtended at the centre ∠AOC= 2 × ∠ADC 90° = 2 × ∠ADC 90 ∴ ∠ADC = \(\frac{90}{2}\)= 45° ∴ ∠ADC = 45°.

In Fig., A, B, and C are three points on a circle with centre O such that ∠BOC = 30° and ∠AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.

Answer»

∠AOB + ∠BOC = 60° + 30° = 90°

∴ ∠AOC = 90°

(Angle subtended at the centre)

∠ADC = ?

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

∴ Angle subtended at the centre

∠AOC= 2 × ∠ADC

90° = 2 × ∠ADC 90

∴ ∠ADC = \(\frac{90}{2}\)= 45°

∴ ∠ADC = 45°.

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In Fig., A, B, and C are three points on a circle with centre O such that ∠BOC = 30° and ∠AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.

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