Ptolemy’s theorem

If ABCD is a cyclic quadrilateralMathworldPlanetmath, then the product of the two diagonals is equal to the sum of the products of opposite sides.


When the quadrilateralMathworldPlanetmath is not cyclic we have the following inequality


An interesting particular case is when both AC and BD are diametersMathworldPlanetmath, since we get another proof of Pythagoras’ theorem.

Title Ptolemy’s theorem
Canonical name PtolemysTheorem
Date of creation 2013-03-22 11:43:13
Last modified on 2013-03-22 11:43:13
Owner drini (3)
Last modified by drini (3)
Numerical id 18
Author drini (3)
Entry type Theorem
Classification msc 51-00
Classification msc 60K25
Classification msc 18-00
Classification msc 68Q70
Classification msc 37B15
Classification msc 18-02
Classification msc 18B20
Related topic CyclicQuadrilateral
Related topic ProofOfPtolemysTheorem
Related topic PtolemysTheorem
Related topic PythagorasTheorem
Related topic CrossedQuadrilateral