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.
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
Michael de Villiers, 15 March 2012.