In the adjoining figure, O is the centre of the circle. If ∠BAO = 60°, then ∠ADC is equal to

1. 30°

2. 45°

3. 60°

4. 120°

In the figure,

OA = OB (Radius of the circle.)

So, △OAB is an isosceles triangle with ∠OBA = ∠BAO (∵ angles opposite to equal sides are equal.)

∠OBA = 60°.

In a triangle the exterior angle is equal to the sum of opposite interior angle.

∴ ∠AOC = ∠BAO + ∠OBA = 60° + 60° = 120°.

Arc AC subtends ∠AOC at centre and ∠ADC at remaining part of circle.

∠AOC = 2∠ADC (∵ angle subtended at centre is double the angle subtended at remaining part of circle.)

120° = 2∠ADC

∠ADC = $\dfrac{120°}{2}$ = 60°.

Hence, Option 3 is the correct option.