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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
Solution
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°
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