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Find de such that [ade]=[debc] and de is minimal

Source: Problem 4, Brazil MO 1992

March 18, 2006
geometrygeometry proposed

Problem Statement

Let ABCABC be a triangle. Find the point DD on its side ACAC and the point EE on its side ABAB such that the area of triangle ADEADE equals to the area of the quadrilateral DEBCDEBC, and the segment DEDE has minimum possible length.
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