For each point in the plane a real number is assigned such that for every triangle its incenter is assigned the mean of the numbers assigned to its vertices.

Prove that the same number is assigned to every point in the plane.

(In reply to Solution. Hope this makes sense. by Jer)

Can you give a solution if the following were added to the problem?

"Degenerate triangles are not recognized when assigning real numbers."

Posted by Bractals on 2011-03-23 16:12:28