Let I, J, K, and L be the incenter and the three excenters of triangle ABC.
What is the center of gravity of these four points?
Initially I noticed that for right triangles the cg was at the midpoint of the hypotenuse. Then I noticed that for other triangles the point was located on the perpendicular bisectors of all the sides, that is, at the circumcenter of the triangle.
Posted by Charlie
on 2008-02-06 12:45:46