Wallace-Simson line | Wallace-Simson theorem

The Simson line is the line containing the feet P_1, P_2, and P_3 of the perpendiculars from an arbitrary point P on the circumcircle of a triangle to the sides or their extensions of the triangle. This line was attributed to Simson by Poncelet, but is now frequently known as the Wallace-Simson line since it does not actually appear in any work of Simson (Johnson 1929, p. 137, p. 41; de Guzmán 1999). The inverse statement to that given above, namely that the locus of all points P in the plane of a triangle Δ A B C such that the feet of perpendiculars from the three sides of the triangle is collinear is given by the circumcircle of Δ A B C, is sometimes called the Wallace-Simson theorem (de Guzmán 1999).

circumcircle | Rigby points | Simson line pole | Steiner deltoid