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. Post a comment or solution.

  Hints: See Problem 54

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