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.