sum of OI^2 independent of triangulation
Source: romania TST 5 / 2007 problem 1
June 13, 2007
geometryincenterinductioncyclic quadrilateralgeometry proposed
Problem Statement
In a circle with center is inscribed a polygon, which is triangulated. Show that the sum of the squares of the distances from to the incenters of the formed triangles is independent of the triangulation.