Ptolemy's theorem

Named after the Greek astronomer and mathematician Ptolemy.

Ptolemy's theorem

1. (geometry) A theorem that states in a cyclic quadrilateral, the product of the lengths of its diagonals is equal to the sum of the products of the lengths of the two pairs of opposite sides.

In mathematical terms, the theorem states if the vertices of a cyclic quadrilateral are A, B, C, and D in order, then ${\displaystyle AC\cdot BD=AB\cdot CD+AD\cdot BC}$.