Let Γ be a parabola with focus F and directrix d.
A line through F intersects Γ in points
P1 and P2.
The feet of the perpendiculars from P1 and P2
d are Q1 and Q2 respectively.
The midpoint of line segment Q1Q2 is
Prove that the rays Q0P1 and
Q0P2 are orthogonal
and that they are tangent to Γ.