Let the opposite sides of a convex Cyclic Hexagon be , , , , , and , and let the
Diagonals , , and be so chosen that , , and have no common
Vertex (and likewise for , , and ), then

This is an extension of Ptolemy's Theorem to the Hexagon.

**References**

Fuhrmann, W. *Synthetische Beweise Planimetrischer Sätze.* Berlin, p. 61, 1890.

Johnson, R. A. *Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.* Boston, MA:
Houghton Mifflin, pp. 65-66, 1929.

© 1996-9

1999-05-26