The Orthopole, the Wallace-Simpson Line, and the Deltoid

Take a point on the circumcircle. Drop perpendiculars to each side. The feet of these perpendiculars are collinear. This line is called the Wallace-Simpson Line. As the point moves along the circumcircle, the envelope of the Wallace-Simpson Lines is a deltoid. Construct a tangent to this point on the circumcircle. The locus of the orthopole of the triangle with respect to this tangent line as the point moves along the circumcircle is the deltoid. To erase the traces, click and drag the background.