Centroids of triangles inscribed/circumscribed to 2 circles.
Source: Moldova 2008 IMO-BMO First TST Problem 3
March 3, 2008
geometrycircumcirclegeometric transformationhomothetysymmetryfunctiongeometry proposed
Problem Statement
Let and denote the incircle and circumcircle, respectively, of a triangle . Consider all the triangels which are simultaneously inscribed in and circumscribed to . Prove that the centroids of these triangles are concyclic.