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 on
d are Q₁ and Q₂ respectively.
The midpoint of line segment Q₁Q₂ is Q₀.

Prove that the rays Q₀P₁ and Q₀P₂ are orthogonal
and that they are tangent to Γ.