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Nagelian point

Source: Iranian National Olympiad (3rd Round) 2002

October 1, 2006
geometryincentercircumcirclevectorsymmetrygeometric transformationhomothety

Problem Statement

H,I,O,NH,I,O,N are orthogonal center, incenter, circumcenter, and Nagelian point of triangle ABCABC. Ia,Ib,IcI_{a},I_{b},I_{c} are excenters of ABCABC corresponding vertices A,B,CA,B,C. SS is point that OO is midpoint of HSHS. Prove that centroid of triangles IaIbIcI_{a}I_{b}I_{c} and SINSIN concide.
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