What are the respective loci of the two De Villiers points if triangle *ABC* is inscribed in a given circle and *BC* is fixed so that only *A* moves along the circumference of the circle?

Use this sketch to investigate by dragging *A* around the circumference of the circle.

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Loci of De Villiers points

What you do observe? Can you prove your observations?

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Michael de Villiers, 24 July 2010.