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computational, perimeter 100, AP/PM = 7/3, incenter related

Source: 2017 Argentina OMA L3 p3

June 19, 2020
geometryperimeterincenter

Problem Statement

Let ABCABC be a triangle of perimeter 100100 and II be the point of intersection of its bisectors. Let MM be the midpoint of side BCBC. The line parallel to ABAB drawn byI I cuts the median AMAM at point PP so that APPM=73\frac{AP}{PM} =\frac73. Find the length of side ABAB.
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