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AE and DI are parallel

Source: Spain Mathematical Olympiad 2021 P6

May 10, 2021
geometryincircleSpainexcircleincenter

Problem Statement

Let ABCABC be a triangle with AB≠ACAB \neq AC, let II be its incenter, γ\gamma its inscribed circle and DD the midpoint of BCBC. The tangent to γ\gamma from DD different to BCBC touches γ\gamma in EE. Prove that AEAE and DIDI are parallel.
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