Fuhrmann's Theorem
Let the opposite sides of a convex Cyclic Hexagon be 
, 
, 
, 
, 
, and 
, and let theDiagonals 
, 
, and 
be so chosen that , , and have no commonVertex (and likewise for , , and ), then
This is an extension of Ptolemy's Theorem to the Hexagon.See also Cyclic Hexagon, Hexagon, Ptolemy's Theorem
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.
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