[SOLVED] Sphere inside a cone

My problem is this:

"Suppose a plane intersects a right-circular cone in a parabola

with vertex V. Suppose that a sphere is inscribed between the

cone and the plane and is tangent to the plane of the parabola at

point F. Show that the chord to the parabola through F which is perpendicular

to FV has length equal to that of the latus rectum of the parabola. Therefore, F is the focus of the parabola."

I have a very hard time trying to see what conditions the sphere puts on the point F.

Anyone?