MathDB
Standard geo

Source: 2023 Japan MO Finals 2

February 11, 2023
geometry

Problem Statement

In an acute triangle ABCABC, let D,E,FD,E,F be the midpoints of BC,CA,ABBC,CA,AB respectively. Let X,YX,Y be the feet of altitude from DD to AB,ACAB,AC respectively. The line through FF parallel to XYXY meets line DYDY at PP. Prove that AD⊥EPAD\perp EP.
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