MathDB

2

Part of 2018 International Olympic Revenge

Problems(1)

Problem 2 IMOR 2018

Source: 2nd IMOR - 2018

7/13/2018
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.
IMORgeometry