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maximum value of the coincident triangle area

Source: China TST 1989, problem 1

June 27, 2005
geometrygeometry unsolved

Problem Statement

A triangle of sides 32,52,2\frac{3}{2}, \frac{\sqrt{5}}{2}, \sqrt{2} is folded along a variable line perpendicular to the side of 32.\frac{3}{2}. Find the maximum value of the coincident area.
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