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exists a triangle with side lengths AU, BV, CW and find it's area

Source: 2005 Austria Beginners' Competition p4

October 12, 2022
geometrytriangle inequalityareas

Problem Statement

We are given the triangle ABCABC with an area of 20002000. Let P,Q,RP,Q,R be the midpoints of the sides BCBC, ACAC, ABAB. Let U,V,WU,V,W be the midpoints of the sides QRQR, PRPR, PQPQ. The lengths of the line segments AUAU, BVBV, CWCW are xx, yy, zz. Show that there exists a triangle with side lengths xx, yy and zz and caluclate it's area.
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