In the figure below, given a triangle
ABC, circumcircle C0, circumradius R, line DEF
parallel to AC and line FGM parallel to AB. C1, C2,
and C3, and R1, R2, and R3
are the circumcircles and circumradii of triangles DBE, FGE, and
MGC respectively, prove that: R // R1 // R2
// R3, and circles C0 and C1
are tangent at B, circles C1 and C2 are
tangent at E, circles C2 and C3 are
tangent at G, and circles C3 and C0 are
tangent at C.
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