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equilateral inside inscribed in a triangle (2015 Kyiv City MO Round2 8.4.1)

Source:

September 4, 2020
geometryequal anglesEquilateral

Problem Statement

On the sides AB,  BC,  CAAB, \, \, BC, \, \, CA of the triangle ABCABC the points C1,  A1,  B1{{C} _ {1}}, \, \, {{A} _ { 1}},\, \, {{B} _ {1}} are selected respectively, that are different from the vertices. It turned out that ΔA1B1C1\Delta {{A} _ {1}} {{B} _ {1}} {{C} _ {1}} is equilateral, ∠BC1A1=∠C1B1A\angle B{{C}_{1}}{{A}_{1}}=\angle {{C}_{1}}{{B}_{1}}A and ∠BA1C1=∠A1B1C\angle B{{A}_{1}}{{C}_{1}}=\angle {{A}_{1}}{{B}_{1}}C . Is ΔABC \Delta ABC equilateral?
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