perplexus.info :: Geometry : Center of Gravity

Center of Gravity (Posted on 2008-02-06)

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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playing with Geometer's Sketchpad (spoiler)

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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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