On Some Properties of the Durairajan Point of a Quadrangle

A number of problems relating to the Durairajan point of a quadrangle which have been proposed by the late Mr. V. Ramaswamy Aiyar [1] do not appear to have been solved so far. While these problems can be dealt with by the familiar methods of synthetic geometry, it is far more instructive to examine them from the higher stand-point of the inversive geometry of the plane. The object of this paper is to follow this line in solving the problems and in deriving therefrom certain interesting results.