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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 + 100180
 OBC + OBC =180  – 100

2OBC = 80                     

 OBC = 40

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