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orthocenter of A_1BC_1 is the incenter of A_2BC_2

Source: III Soros Olympiad 1996-97 R1 9.6 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 29, 2024
geometryincenterorthocenter

Problem Statement

In triangle ABCABC, angle BB is not right. The circle inscribed in ABCABC touches ABAB and BCBC at points C1C_1 and A1A_1, and the feet of the altitudes drawn to the sides ABAB and BCBC are points C2C_2 and A2A_2. Prove that the intersection point of the altitudes of triangle A1BC1A_1BC_1 is the center of the circle inscribed in triangle A2BC2A_2BC_2.
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