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locus of circumcenters of similar triangles, Austrian-Polish 2000

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May 19, 2019
geometrysimilar trianglesLocuscircumcircle

Problem Statement

Triangle A0B0C0A_0B_0C_0 is given in the plane. Consider all triangles ABCABC such that: (i) The lines AB,BC,CAAB,BC,CA pass through C0,A0,B0C_0,A_0,B_0, respectvely, (ii) The triangles ABCABC and A0B0C0A_0B_0C_0 are similar. Find the possible positions of the circumcenter of triangle ABCABC.
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