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Question

O is the centre of the circle. If BAC= 50, find ∠OBC.


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Solution

Given: In a circle with centre at O BAC = 50.

To find: OBC = ?

Procedure: BAC = 50
∠ BOC = 2BAC = 2(50) =100
(Arc BC subtends BOC at the centre and BAC at remaining part of circle)
In OBC, OB = OC = radius
OBC = OCB (Opposite angles of equal sides of a Δ)
Now, OBC + OCB + BOC = 180 (Sum of angles in a triangle)
OBC + OCB + 100= 180
OBC + OBC =180100

2OBC = 80

OBC = 40


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