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Trivial geo as #2

Source: IOM 2021 #2

December 8, 2021
geometryconcurrency

Problem Statement

Points PP and QQ are chosen on the side BCBC of triangle ABCABC so that PP lies between BB and QQ. The rays APAP and AQAQ divide the angle BACBAC into three equal parts. It is known that the triangle APQAPQ is acute-angled. Denote by B1,P1,Q1,C1B_1,P_1,Q_1,C_1 the projections of points B,P,Q,CB,P,Q,C onto the lines AP,AQ,AP,AQAP,AQ,AP,AQ, respectively. Prove that lines B1P1B_1P_1 and C1Q1C_1Q_1 meet on line BCBC.
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