  The lengths of geodesics on hyperbolic surfaces satisfy intriguing equations,
known as identities, relating these lengths to geometric quantities of the
surface. This paper is about a large family of identities that relate lengths
of closed geodesics and orthogeodesics to boundary lengths or number of cusps.
These include, as particular cases, identities due to Basmajian, to McShane and
to Mirzakhani and Tan-Wong-Zhang. In stark contrast to previous identities, the
identities presented here include the lengths taken among all closed geodesics.
