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FX and BZ meet at w

Source: Own. Malaysian IMO TST 2022 P6

May 13, 2022
geometry

Problem Statement

Given a triangle ABCABC with AB=ACAB=AC and circumcenter OO. Let DD and EE be midpoints of ACAC and ABAB respectively, and let DEDE intersect AOAO at FF. Denote ω\omega to be the circle (BOE)(BOE). Let BDBD intersect ω\omega again at XX and let AXAX intersect ω\omega again at YY.
Suppose the line parallel to ABAB passing through OO meets CYCY at ZZ. Prove that the lines FXFX and BZBZ meet at ω\omega.
Proposed by Ivan Chan Kai Chin
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