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In triangle with |AB| > |AC|, find angle BAC

Source: 2022 Abelkonkurransen Finale, Problem 2a

March 12, 2024
geometryAngle Chasingharmonic division

Problem Statement

A triangle ABCABC with circumcircle ω\omega satisfies ∣AB∣>∣AC∣|AB| > |AC|. Points XX and YY on ω\omega are different from AA, such that the line AXAX passes through the midpoint of BCBC, AYAY is perpendicular to BCBC, and XYXY is parallel to BCBC. Find ∠BAC\angle BAC.
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