MathDB
Question 5

Source: Iran TST 2006

April 30, 2006
geometrycircumcircletrigonometryinequalitiesfunctionincentergeometry proposed

Problem Statement

Let ABCABC be an acute angle triangle. Suppose that D,E,FD,E,F are the feet of perpendicluar lines from A,B,CA,B,C to BC,CA,ABBC,CA,AB. Let P,Q,RP,Q,R be the feet of perpendicular lines from A,B,CA,B,C to EF,FD,DEEF,FD,DE. Prove that 2(PQ+QR+RP)≥DE+EF+FD 2(PQ+QR+RP)\geq DE+EF+FD
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