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Parallel lines

Source: India RMO 1991 Problem 5

October 15, 2005
geometryparallelogram

Problem Statement

Take any point P1P_1 on the side BCBC of a triangle ABCABC and draw the following chain of lines: P1P2P_1P_2 parallel to ACAC; P2P3P_2P_3 parallel to BCBC; P3P4P_3P_4 parallel to ABAB ; P4P5P_4P_5 parallel to CACA; and P5P6P_5P_6 parallel to BCBC, Here, P2,P5P_2,P_5 lie on ABAB; P3,P6P_3,P_6 lie on CACA and P4P_4 on BCBC> Show that P6P1P_6P_1 is parallel to ABAB.
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