MathDB

4

Part of 2005 Austria Beginners' Competition

Problems(1)

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

Source: 2005 Austria Beginners' Competition p4

10/12/2022
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.
geometrytriangle inequalityareas