Let the opposite sides of a convex cyclic hexagon be polygon diagonals polygon vertex
(and likewise for
This is an extension of Ptolemy's theorem to
the hexagon .
See also Cyclic Hexagon ,
Hexagon ,
Ptolemy's Theorem
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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. Referenced on Wolfram|Alpha Fuhrmann's Theorem
Cite this as:
Weisstein, Eric W. "Fuhrmann's Theorem."
From MathWorld https://mathworld.wolfram.com/FuhrmannsTheorem.html
Subject classifications
,
, 
, 
, 
, and 
, and let the polygon diagonals 
, 
, and 
be so chosen that 
, 
, and 
have no common polygon vertex
(and likewise for 
,
,
and 
),
then
