MathDB

circumcenter of ABC lies on PA All-Russian MO 2005 Regional (R4) 8.4

Source:

August 26, 2024

geometrycollinear

Problem Statement

Given an acute triangle

ABC

. Points

B'

and

C'

are symmetrical, respectively, to vertices

B

and

C

wrt straight lines

AC

and

AB

. Let

P

be the intersection point of the circumcircles of triangles

ABB'

and

ACC'

, different from

A

. Prove that the center of the circumcircle of triangle

ABC

lies on line

PA