MathDB
Triangle

Source: Iran TST 2002

September 27, 2006
geometrycircumcircleperimetergeometry proposed

Problem Statement

OO is a point in triangle ABCABC. We draw perpendicular from OO to BC,AC,ABBC,AC,AB which intersect BC,AC,ABBC,AC,AB at A1,B1,C1A_{1},B_{1},C_{1}. Prove that OO is circumcenter of triangle ABCABC iff perimeter of ABCABC is not less than perimeter of triangles AB1C1,BC1A1,CB1A1AB_{1}C_{1},BC_{1}A_{1},CB_{1}A_{1}.
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