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Geometry Problem

Source: SRMC 2022 P1

May 23, 2022
geometry

Problem Statement

Convex quadrilateral ABCDABCD is inscribed in circle w.w.Rays ABAB and DCDC intersect at K. LK.\ L is chosen on the diagonal BDBD so that ∠BAC=∠DAL. M\angle BAC= \angle DAL.\ M is chosen on the segment KLKL so that CM∣∣BD.CM \mid\mid BD. Prove that line BMBM touches w.w. (Kungozhin M.)
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