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3 lines concurrent with a circle

Source: TOT 327 1992 Spring Α J4 - Tournament of Towns

June 9, 2024
geometryconcurrency

Problem Statement

Let PP be a point on the circumcircle of triangle ABCABC. Construct an arbitrary triangle A1B1C1A_1B_1C_1 whose sides A1B1A_1B_1, B1C1B_1C_1 and C1A1C_1A_1 are parallel to the segments PCPC, PAPA and PBPB respectively and draw lines through the vertices A1A_1, B1B_1 and C1C_1 and parallel to the sides BCBC, CACA and ABAB respectively. Prove that these three lines have a common point lying on the circumcircle of triangle A1B1C1A_1B_1C_1.
(V. Prasolov)
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