#### 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 ∠AOB

= `1/2 xx108°`

= 54°

Now, Arc BC subtends ∠BOC at the centre and

∠CAB at the remaining part of the circle.

∴ `∠CAB = 1/2 ∠BOC`

=` 1/2xx 54°`

= 27°

Is there an error in this question or solution?

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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: Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.

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