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Perpendicular bisectors and concyclic

Source: Japan TST 2019 P8

January 24, 2021
geometryperpendicular bisectorcircumcircleHi

Problem Statement

In acute triangle △ABC\triangle ABC, OO is its circumcenter, and points D,ED,E lie on sides AB,ACAB,AC (excluding endpoints) such that BC,DEBC,DE are not parallel. Line BCBC meet DEDE at FF, and the perpendicular bisectors of BD,CEBD,CE meet at KK. KOKO meets BCBC at LL and AOAO meets DEDE at MM. Prove that F,M,L,OF,M,L,O are concyclic.
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