The requested f becomes the product of reflections f = g*e*c*a. For circular quadrangles this is always a translation. In particular this translation preserves the points of the first side AD, hence it is parallel to it (we rotate counterclockwise successively about A, B, C and D).

In particular, when the original quadrangle ABCD accepts an inscribed circle, then m = 0, and for every X, f(X) = X.

This problem is consdered in the file: RotationsOnQuadrangleVerticesCircum.html .

A related subject, resulting by replacing rotations with reflexions is handled in the file: ReflectingOnPolygonSides.html .

For an application on circular-arcs-polygons, inscribed in other polygons look at the file: SuccessiveArcsPath.html .

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