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DEF, ABC similar iff ABC equilateral, incircle - 1993 Cono Sur Shortlist G8

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October 24, 2021
geometrysimilar trianglesincircleEquilateral

Problem Statement

In a triangle ABCABC, let DD, EE and FF be the touchpoints of the inscribed circle and the sides ABAB, BCBC and CACA. Show that the triangles DEFDEF and ABCABC are similar if and only if ABCABC is equilateral.
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