MathDB
Perpendicular lines

Source: RMO 2019 P5

October 20, 2019
geometryRMO

Problem Statement

In an acute angled triangle ABCABC, let HH be the orthocenter, and let D,E,FD,E,F be the feet of altitudes from A,B,CA,B,C to the opposite sides, respectively. Let L,M,NL,M,N be the midpoints of the segments AH,EF,BCAH, EF, BC respectively. Let X,YX,Y be the feet of altitudes from L,NL,N on to the line DFDF respectively. Prove that XMXM is perpendicular to MYMY.
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