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: ∠CAB

Answer 1

Join AD and DB

Arc B = 2 arc BC and ∠AOB = 180°

∴ ∠BOC = `1/2` ∠AOB

= `1/2 xx 108^circ`

= 54°

Now, Arc BC subtends ∠BOC at the centre and ∠CAB at the remaining part of the circle.

∴ ∠CAB = `1/2` ∠BOC

= `1/2 xx 54^circ`

= 27°