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one side of triangle is twice as another, AI=MI, incenter related

Source: Czech-Polish-Slovak Junior Match 2015, Team p1 CPSJ

March 19, 2020
geometryincenter

Problem Statement

Let II be the center of the circle of the inscribed triangle ABCABC and MM be the center of its side BCBC. If ∣AI∣=∣MI∣|AI| = |MI|, prove that there are two of the sides of triangle ABCABC, of which one is twice of the other.
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