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triangleABC BC=1/2(AB+AC)

Source: Bosnia and Herzegovina 2011

May 16, 2011
geometryincentercircumcirclegeometric transformationhomothetyratioanalytic geometry

Problem Statement

In triangle ABCABC it holds ∣BC∣=12(∣AB∣+∣AC∣)|BC|= \frac{1}{2}(|AB|+|AC|). Let MM and NN be midpoints of ABAB and ACAC, and let II be the incenter of ABCABC. Prove that A,M,I,NA, M, I, N are concyclic.
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