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Inscribed hexagon

Source: 239 2008 J4

July 28, 2020
geometry

Problem Statement

Point PP is located inside an acute-angled triangle ABCABC. A1A_1, B1B_1, C1C_1 are points symmetric to PP with respect to the sides of triangle ABCABC. It turned out that the hexagon AB1CA1BC1AB_1CA_1BC_1 is inscribed. Prove that PP is the Torricelli point of triangle ABCABC.
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