Question

In the following figure, O is centre of the circle and ΔABC is equilateral.

Find: 

1. ∠ADB,
2. ∠AEB.

Answer 1

Since ∠ACB and ∠ADB are in the same segment,

∠ADB = ∠ACB = 60°

Join OA and OB

Here, ∠AOB = 2∠ACB

= 2 × 60°

= 120°

`∠AEB = 1/2  "Reflex"  (∠AOB) = 1/2 (360^circ - 120^circ) = 120^circ`

(Angle at the centre is double the angle at the circumference subtended by the same chord)