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Bisectors of a triangle

Source: 2011 Sharygin Geometry Olympiad #4

May 22, 2014
geometrygeometric transformationreflectioninequalitiestriangle inequalitygeometry unsolved

Problem Statement

Segments AA′AA', BB′BB', and CC′CC' are the bisectrices of triangle ABCABC. It is known that these lines are also the bisectrices of triangle A′B′C′A'B'C'. Is it true that triangle ABCABC is regular?
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