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DE + DF <= BC , 3 altitudes

Source: 2007 Indonedia MO Province P2 q4 OSP

December 11, 2020
geometrygeometric inequalityaltitudes

Problem Statement

In acute triangles ABCABC, AD,BE,CFAD, BE ,CF are altitudes, with D,E,FD, E, F on the sides BC,CA,ABBC, CA, AB, respectively. Prove that DE+DF≤BCDE + DF \le BC
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