Question below?

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1 Answer
Apr 6, 2018

Please see below.

Explanation:

The problem is as shown below.
enter image source here

In this figure, as #BC# bisects #/_ABQ#, #m/_ABC=m/_CBQ=x#

Now according to alternate segment theorem (also known as the tangent-chord theorem) - in any circle, the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.

therefore #m/_CBQ=m/_BAC=x#

and in #DeltaABC#, #m/_BAC=m/_ABC=x#

as two angles of #DeltaABC# areequal, it is an isosceles trangle

and hence opposites are equal i.e. #AC=BC#.