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incenters not collinear, equal angles (I Soros Olympiad 1994-95 R1 9.7 10.7)

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July 31, 2021
geometryincentercollinearequal angles

Problem Statement

Given an acute triangle ABCABC, in which ∠BAC<30o\angle BAC <30^o. On sides ACAC and ABAB are taken respectively points DD and EE such that ∠BDC=∠BDE=∠ADE=60o\angle BDC=\angle BDE = \angle ADE = 60^o. Prove that the centers of the circles. inscribed in triangles ADEADE, BDEBDE and BCDBCD do not lie on the same line.
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