MathDB
Geometry Problem

Source: Federal Mathematical Competition of Serbia and Montenegro 2004

May 14, 2018
geometry

Problem Statement

In a triangle ABCABC of the area SS, point HH is the orthocenter, D,E,FD,E,F are the feet of the altitudes from A,B,CA,B,C, and P,Q,RP,Q,R are the reflections of A,B,CA,B,C in BC,CA,ABBC,CA,AB, respectively. The triangles DEFDEF and PQRPQR have the same area TT. Given that T>35ST > \frac{3}{5}S, prove that T=ST = S.
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