Mr. Gibbins’ paper on the “Feuerbach Quadrilateral” ( Math. Gazette , No. 249) deals with a delightful topic. The device employed is certainly ingenious. May I, however, be permitted to discuss the topic from an entirely different point of view, but with the same object in mind, namely of stimulating our pupils’ interest in Analytical Geometry I shall also bring out some interesting properties of the diagonal triangles and the diagonal-point triangles of certain quadrilaterals associated with a triangle, employing general rather than special methods to arrive at the results.