Ptolemy's theorem

Ptolemy's theorem gives a special relationship between the sides and diagonals of a cyclic quadrilateral (a quadrilateral whose vertices all lie on a circle). It states that for such a quadrilateral, the product of the lengths of its diagonals equals the sum of the products of its two pairs of opposite sides.

Important properties

• Applies only to cyclic quadrilaterals.

• If the quadrilateral is not cyclic, the equality does not hold.

• The theorem can be used to compute unknown side or diagonal lengths if the others are known.

• It generalizes the Pythagorean theorem (which is the special case when the quadrilateral is a rectangle).