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Problem 2 IMOR 2018

Source: 2nd IMOR - 2018

July 13, 2018
IMORgeometry

Problem Statement

Let GG be the centroid of a triangle △ABC\triangle ABC and let AG,BG,CGAG, BG, CG meet its circumcircle at P,Q,RP, Q, R respectively. Let AD,BE,CFAD, BE, CF be the altitudes of the triangle. Prove that the radical center of circles (DQR),(EPR),(FPQ)(DQR),(EPR),(FPQ) lies on Euler Line of △ABC\triangle ABC.
Proposed by Ivan Chai, Malaysia.
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