Let A be a point outside circle Γ. Let B and C be points
where lines through A are tangent to Γ. Let D be a point
on line BC outside Γ. Let E and F be points where lines
through D are tangent to Γ.

     1) Prove that A, E, and F are collinear.

Let G be the intersection of chords BC and EF. Let PQ
be any chord of Γ passing through G.

     2) Prove that the intersection of lines
         AP and DQ lies on Γ.
  

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