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NMO (Nepal) Problem 3

Source:

March 17, 2024
geometry

Problem Statement

Let ABCABC be an acute triangle and HH be its orthocenter. Let EE be the foot of the altitude from CC to ABAB, FF be the foot of the altitude from BB to ACAC. Let G≠HG \neq H be the intersection of the circles (AEF)(AEF) and (BHC)(BHC). Prove that AGAG bisects BCBC.
Proposed by Kang Taeyoung, South Korea
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