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.
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.