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equal segments wanted, line connecting incenters related, altitudes

Source: 239 MO VIII-IX 2000 p3

May 12, 2020
geometryincenteraltitudeequal segments

Problem Statement

Let AA1 AA_1 and CC1 CC_1 be the altitudes of the acute-angled triangle ABC ABC . A line passing through the centers of the inscribed circles the triangles AA1C AA_1C and CC1A CC_1A intersect the sides of AB AB and BC BC triangle ABC ABC at points X X and Y Y . Prove that BX=BY BX = BY .
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