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In any triangle ABC, if the angle bisec...

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

Text Solution

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Angle bisector`angleA`meets the circumcircle of triangleABC at point P
from diagram
`angleBAD=angleCAD`
so, ABD is a Cyclic Quadrilateral
`angleDBC=angleDAC=1/2angleA`
`angleDCB=angle BAD=1/2angleA`
`angleDBC=angleDCB`
`In triangleDCB`
...
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