Fuhrmann's Theorem


Let the opposite sides of a convex cyclic hexagon be a, a^', b, b^', c, and c^', and let the polygon diagonals e, f, and g be so chosen that a, a^', and e have no common polygon 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

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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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Fuhrmann's Theorem

Cite this as:

Weisstein, Eric W. "Fuhrmann's Theorem." From MathWorld--A Wolfram Web Resource.

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