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M,N interior points of triangle ABC, prove that AN>AM or BN>BM or CN>CM

Source: Tuymaada 1994 p3

September 28, 2018
geometrygeometric inequality

Problem Statement

Point MM lies inside triangle ABCABC. Prove that for any other point NN lying inside the triangle ABCABC, at least one of the following three inequalities is fulfilled: AN>AM,BN>BM,CN>CMAN>AM, BN>BM, CN>CM.
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