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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: - ICSE Class 10 - Mathematics

ConceptArc 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

#### 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:

#### Solution

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°

(ii) 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