Casey's theorem and its converse can be used to prove a variety of statements in Euclidean geometry.

Such a configuration is also the basis for Casey's theorem, itself a generalization of Ptolemy's theorem.

He is most famous for Casey's theorem on a circle that is tangent to four other circles, an extension of the problem of Apollonius.

In mathematics, Casey's theorem, also known as the generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish mathematician John Casey.