Lambert's Theorem : circumcircle of a triangle tangent to a parabola

Lambert's theorem

The circumcircle of a triangle formed by three tangents to a parabola, passes through the focus of the parabola. This applet lets you move the tangent points A, B, C. It shows the triangle PQR and its circumcircle which goes through the focus F of the parabola. If you slide the green cursor, you will have a proof without words in 22 steps.