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collinear wanted, angle bisector, 2 parallel, 1 perpendicular

Source: Indonesia INAMO Shortlist 2009 G1 https://artofproblemsolving.com/community/c1101409_

December 10, 2021
collineargeometryangle bisector

Problem Statement

Given triangle ABCABC, ALAL bisects angle ∠BAC\angle BAC with LL on side BCBC. Lines LRLR and LSLS are parallel to BABA and CACA respectively, RR on side ACAC andS S on side ABAB, respectively. Through point BB draw a perpendicular on ALAL, intersecting LRLR at MM. If point DD is the midpoint of BCBC, prove that that the three points A,M,DA, M, D lie on a straight line.
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