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minimal sum of areas of triangles insides a rectangle

Source: May Olympiad (Olimpiada de Mayo) 1996 L2

September 15, 2018
geometryrectangleareas

Problem Statement

Let ABCDABCD be a rectangle. A line rr moves parallel to ABAB and intersects diagonal ACAC , forming two triangles opposite the vertex, inside the rectangle. Prove that the sum of the areas of these triangles is minimal when rr passes through the midpoint of segment ADAD .
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