Centroids

The Problem :

Using Cabri-Géomètrie, or Geometers’ SketchPad, construct a circle of convenient size and a triangle whose vertices lie on the circle. Construct the centroid of the triangle by joining each vertex of the triangle to the mid-point of the opposite side. What are the three loci of the centroid as each vertex of the triangle is allowed to move around the circle in turn?

Prove your results.

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Last modified: June 18, 2007