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Question

In any triangle ABC, if the angle bisector of angle A and perpendicular bisector  of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.


Solution


We prove this individually 
Let angular bisector of A meet the circumcircle at T. 
Join BT&CT
BAT=BCT=α (angle same segment of BT)
Similarly CBT=TAC=α("of CT)
CBT=BCT=
ΔTBC is isosceless
Any \perp r from T on BC will bisect it
angular insector of A& r bisector of BC at a point on circum centre.

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