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Ptolemy's Theorem


If a Quadrilateral is inscribed in a circle (i.e., for a cyclic quadrilateral), the sum of the products of the two pairs of opposite sides equals the product of the diagonals

AB\times CD+BC\times DA=AC\times BD.

This fact can be used to derive the Trigonometry addition formulas.

See also Fuhrmann's Theorem, Ptolemy Inequality


Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 42-43, 1967.

© 1996-9 Eric W. Weisstein