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"Incentric" rectangle in trapezoid

Source: Czech and Slovak Olympiad 1978, National Round, Problem 5

October 11, 2024
geometrytrapezoidincenterrectangleIsosceles Trapezoid

Problem Statement

Let ABCSABCS be an isosceles trapezoid. Denote A′,B′,C′,D′A',B',C',D' the incenters of triangles BCD,CDA,BCD,CDA, DAB,ABC,DAB,ABC, respectively. Show that A′,B′,C′,D′A',B',C',D' are vertices of a rectangle.
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