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Source: Romania EGMO TST 2021 Day 2 P2

November 23, 2022
geometryromania

Problem Statement

Through the midpoint MM of the side BCBC of the triangle ABCABC passes a line which intersects the rays ABAB and ACAC at DD and EE, respectively, such that AD=AEAD=AE. Let FF be the foot of the perpendicular from AA onto BCBC and PP{} the circumcenter of triangle ADEADE. Prove that PF=PMPF=PM.
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