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In the figure below, the circles of centers O and A are tangent at B, the circles O and F are tangent at G. A chord CD of the circle O is tangent to the circle A at E and tangent to the circle F at H. BE and DG meet at a point P and BC and GH meet at Q. Prove that the quadrilateral BPQG is a cyclic quadrilateral.
 

  Hints: See Problem 54

I have used Geometry Expressions to visualize these geometric forms and check out a variety of conjectures. Geometry Expressions is the world's first Interactive Symbolic Geometry System. This means: Geometric figures can be defined by either Symbolic Constraints or numeric locations.