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(MB- MS)(NC-NS) <= 0, midpoints (Kyiv City Olympiad 2010 8.5)

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July 2, 2020
geometrymidpointsgeometric inequality

Problem Statement

In an acute-angled triangle ABCABC, the points MM and NN are the midpoints of the sides ABAB and ACAC, respectively. For an arbitrary point SS lying on the side of BCBC prove that the condition holds (MB−MS)(NC−NS)≤0(MB- MS)(NC-NS) \le 0
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