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Orthogonal Tangents (Posted on 2011-11-30) Difficulty: 3 of 5
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.

See The Solution Submitted by Bractals    
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re: solution Comment 2 of 2 |
(In reply to solution by Daniel)

Now the next part - prove that they are tangent to the parabola.
  Posted by Bractals on 2011-12-01 17:11:27

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