The following note may be considered as an addendum to the paper by me on pp. 42–47 of this volume of the Proceedings. In that paper it is shown how to inscribe in a triangle ABC, a triangle DEF, such that the perpendiculars to the sides of ABC, drawn through the points D, E, F, shall be concurrent in a point P. This is done by constructing on each of the sides of ABO a triangle similar to DEF; then O the point of concurrence of the three lines joining the vertices of ABC to the vertices of these triangles is the point “inverse” to P. The question, then, naturally arises, What must be the shape of the triangle DEF in order that the point P may be one of the Brocard points, and, as a consequence, O the other one? and the answer is easily seen to be that DEF must be similar to ABO. Hence the following construction:—