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2010 Geometry #8: Maximum Area of Triangle

Source:

February 14, 2015
geometry

Problem Statement

Let OO be the point (0,0)(0,0). Let AA, BB, CC be three points in the plane such that AO=15AO=15, BO=15BO = 15, and CO=7CO = 7, and such that the area of triangle ABCABC is maximal. What is the length of the shortest side of ABCABC?
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