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BY, CX, AH are concurrent

Source: ARO Regional stage 2023 11.5

February 16, 2023
geometryRussia

Problem Statement

Given is a triangle ABCABC with altitude AHAH and median AMAM. The line OHOH meets AMAM at DD. Let AB∩CD=E,AC∩BD=FAB \cap CD=E, AC \cap BD=F. If EHEH and FHFH meet (ABC)(ABC) at X,YX, Y, prove that BY,CX,AHBY, CX, AH are concurrent.
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