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Prove that BN<IM

Source: 2009 Peru Iberoamerican TST problem 4

May 8, 2023
geometry

Problem Statement

Let ABCABC be a triangle such that AB<BCAB < BC. Plot the height BHBH with HH in ACAC. Let I be the incenter of triangle ABCABC and MM the midpoint of ACAC. If line MIMI intersects BHBH at point NN, prove that BN<IMBN < IM.
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