The Simson line is the Line containing the feet of the perpendiculars from a point on the Circumcircle of a Triangle to the sides (or their extensions) of the Triangle. The Simson line is sometimes known as the Wallace-Simson Line, since it does not appear in any work of Simson (Johnson 1929, p. 137).

The Angle between the Simson lines of two points and is half the Angle of the arc . The Simson line of any Vertex is the Altitude through that Vertex. The Simson line of a point opposite a Vertex is the corresponding side. If is the Simson line of a point of the Circumcircle, then the triangles and are directly similar.

**References**

Coxeter, H. S. M. and Greitzer, S. L. *Geometry Revisited.* Washington, DC: Math. Assoc. Amer.,
pp. 40-41 and 43-45, 1967.

Johnson, R. A. *Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.*
Boston, MA: Houghton Mifflin, pp. 137-139, 1929.

© 1996-9

1999-05-26