Eight and seven point degenerations of Miquel's Theorem in Laguerre planes

Abstract.

For Möbius planes Schaeffer [9] has proved that all seven point degenerations of Miquel's Theorem characterize miquelian Möbius planes. For Laguerre planes we have several degenerations of Miquel's Theorem with eight and seven points. We prove that all except one of these degenerations characterize miquelian Laguerre planes. The remaining degeneration characterizes elation Laguerre planes.