MathDB
circumcenters of two triangles

Source: Croatian NMC 2005, 2nd Grade

May 8, 2007
geometrycircumcircleincentergeometric transformationhomothetygeometry proposed

Problem Statement

Let UU be the incenter of a triangle ABCABC and O1,O2,O3O_{1}, O_{2}, O_{3} be the circumcenters of the triangles BCU,CAU,ABUBCU, CAU, ABU , respectively. Prove that the circumcircles of the triangles ABCABC and O1O2O3O_{1}O_{2}O_{3} have the same center.
Back to ProblemsView on AoPS