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Center of Gravity (Posted on 2008-02-06) Difficulty: 3 of 5
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?

See The Solution Submitted by Bractals    
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Solution playing with Geometer's Sketchpad (spoiler) | Comment 1 of 7
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
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