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Circles through vertices tangent to the incircle

Source: KoMaL A. 845

March 11, 2023
geometrykomal

Problem Statement

The incircle of triangle ABCABC is tangent to sides BCBC, ACAC, and ABAB at points DD, EE and FF, respectively. Let A′A' denote the point of the incircle for which circle (A′BC)(A'BC) is tangent to the incircle. Define points B′B' and C′C' similarly. Prove that lines A′DA'D, BE′BE', and CF′CF' are concurrent.
Proposed by Áron Bán-Szabó, Budapest
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