## Parabola circumcircle theorem

Three tangents to a parabola with focus *F* are constructed to form a triangle *ABC* as shown. What do you notice about the circumcircle of triangle *ABC*? Drag either of points *X*, *Y* or *Z* to check your observation.

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Parabola circumcircle theorem

Can you explain why (prove that) the circumcircle of *ABC* always passes through the focus *F* of the parabola? If stuck, click on Hint

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Michael de Villiers, 15 March 2012.