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Fuhrmann's Theorem


Let the opposite sides of a convex Cyclic Hexagon be $a$, $a'$, $b$, $b'$, $c$, and $c'$, and let the Diagonals $e$, $f$, and $g$ be so chosen that $a$, $a'$, and $e$ have no common Vertex (and likewise for $b$, $b'$, and $f$), then


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

See also Cyclic Hexagon, Hexagon, Ptolemy's Theorem


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 Eric W. Weisstein