Question

In the figure, O is the centre of the circle and the length of arc AB is twice the length of arc BC. If angle AOB = 108°, find: ∠ADB.

Answer 1

Again, Arc AB subtends ∠AOB at the centre and

∠ACB at the remaining part of the circle.

∠ ACB = `1/2` ∠AOB

=` 1/2 xx 108°`

= 54
In cyclic quadrilateral ADBC

∠ADB + ∠ACB = 180°   ...[sum of opposite angles]

⇒ ∠ADB + 54° = 180°

⇒ ∠ADB = 180° − 54°

⇒ ∠ADB = 126°