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Two midperpendiculars

Source: 2011 Sharygin Geometry Olympiad #3

May 22, 2014
geometrygeometric transformationreflectionangle bisectorgeometry unsolved

Problem Statement

Let ABCABC be a triangle with ∠A=60∘\angle{A} = 60^\circ. The midperpendicular of segment ABAB meets line ACAC at point C1C_1. The midperpendicular of segment ACAC meets line ABAB at point B1B_1. Prove that line B1C1B_1C_1 touches the incircle of triangle ABCABC.
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