WOLFRAM|DEMONSTRATIONS PROJECT

Ptolemy's Theorem

​
AB
×
CD
+
BC
×
DA
=
3.696
AC
×
BD
=
3.696
Let ABCD be a quadrilateral where all the vertices lie on a circle. As long as the (green) diagonals cross,
AB×CD+BC×DA=AC×BD
; in words, the sum of the products of the two pairs of opposite sides equals the product of the diagonals.
Drag any vertex to another location on the circle.