Converse of a theorem for parabolas

Question

I have heard about the theorem that tangents drawn at the extremities of the focal chord intersect on the directrix. Is the converse of the theorem also true ? i.e., is the following statement true “If two tangents drawn to a parabola are at right angles to each other , their chord of contact will always be the focal chord”? I know that the locus of the point of intersection of perpendicular tangents to a parabola is called the director’s circle, so obviously , any perpendicular tangents will always intersect in the directors circle.