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perpendicular medians in a triangle with given third side and area

Source: Mexican Mathematical Olympiad 1989 OMM P1

July 27, 2018
geometryMediansarea of a triangleperpendicular

Problem Statement

In a triangle ABCABC the area is 1818, the length ABAB is 55, and the medians from AA and BB are orthogonal. Find the lengths of the sides BC,ACBC,AC.
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