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BD=2 EN if CD // ME , AM=//MB, AN=//NC

Source: Greece Junior Math Olympiad 2023 p2

March 2, 2024
equal segmentsgeometry

Problem Statement

In triangle ABCABC, points MM, NN are the midpoints of sides ABAB, ACAC respelctively. Let DD and EE be two points on line segment BNBN such that CD∥MECD \parallel ME and BD<BEBD <BE. Prove that BD=2⋅ENBD=2\cdot EN.
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