MathDB
N-secting a,b,c gives a rational expression

Source: IberoAmerican 1988 Q4

December 13, 2010
geometry proposedgeometry

Problem Statement

△ABC\triangle ABC is a triangle with sides a,b,ca,b,c. Each side of △ABC\triangle ABC is divided in nn equal segments. Let SS be the sum of the squares of the distances from each vertex to each of the points of division on its opposite side. Show that Sa2+b2+c2\frac{S}{a^2+b^2+c^2} is a rational number.
Back to ProblemsView on AoPS