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P3 froncophone

Source: P3 : froncophone math olympiad junior 2022

May 23, 2022
geometry

Problem Statement

Let △ABC\triangle ABC a triangle, and DD the intersection of the angle bisector of ∠BAC\angle BAC and the perpendicular bisector of ACAC. the line parallel to ACAC passing by the point BB, intersect the line ADAD at XX. the line parallel to CXCX passing by the point BB, intersect ACAC at YY. E=(AYB)∩BXE = (AYB) \cap BX . prove that CC , DD and EE collinear.
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