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PQ//BC wanted, projections of A on angle bisectors

Source: Indonesia INAMO Shortlist 2017 G3 https://artofproblemsolving.com/community/c1101409_indonesia_shortlist__geometry

November 15, 2021
geometryparallel

Problem Statement

In triangle ABCABC, points PP and QQ are projections of point AA onto the bisectors of angles ABCABC and ACBACB, respectively. Prove that PQ∥BCPQ\parallel BC.
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