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Intouch triangle is acute

Source: 2006 Swedish Mathematical Competition #2

January 5, 2018
geometryincenterSweden

Problem Statement

In a triangle ABCABC, point PP is the incenter and A′A', B′B', C′C' its orthogonal projections on BCBC, CACA, ABAB, respectively. Show that ∠B′A′C′\angle B'A'C' is acute.
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