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AP passes through circumcenter of ABC, points symmetric wrt sides

Source: 2010 Croatia MO (pre-TST) p7

August 5, 2020

geometrycircumcircleCircumcentercollinear

Problem Statement

Given a non- isosceles triangle

ABC

. Let the points

B'

and

C'

be symmetric to the points

B

and

C

wrt

AC

and

AB

respectively. If the circles circumscribed around triangles

ABB'

and

ACC'

intersect at point

P

, prove that the line

AP

passes through the center of the circumcircle of the triangle

ABC