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Geo with angle bisector

Source: Czech-Polish-Slovak Match 2022 P5

September 3, 2022
geometryangle bisector

Problem Statement

Let ABCABC be a triangle with AB<ACAB < AC and circumcenter OO. The angle bisector of ∠BAC\angle BAC meets the side BCBC at DD. The line through DD perpendicular to BCBC meets the segment AOAO at XX. Furthermore, let YY be the midpoint of segment ADAD. Prove that points B,C,X,YB, C, X, Y are concyclic.
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