Simson Line

The Simson line is the Line containing the feet of the perpendiculars from a point on the Circumcircle of aTriangle to the sides (or their extensions) of the Triangle. The Simson line is sometimes known as theWallace-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 Simsonline of any Vertex is the Altitude through that Vertex. TheSimson line of a point opposite a Vertex is the corresponding side. If is the Simsonline 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.

• Skew Polyomino
• Skew Quadrilateral
• Skew Symmetric Matrix
• Sklar's Theorem
• Skolem-Mahler-Lerch Theorem
• Skolem Paradox
• Skolem Sequence
• Slant Height
• Slice Knot
• Slide Move
• Slide Rule
• Slightly Defective Number
• Slightly Excessive Number
• Slip Knot
• Slope
• Slothouber-Graatsma Puzzle
• Slutzky-Yule Effect
• Sluze Pearls
• Smale-Hirsch Theorem
• Smale Horseshoe Map
• Small Cubicuboctahedron
• Small Ditrigonal Dodecacronic Hexecontahedron
• Small Ditrigonal Dodecicosidodecahedron
• Small Ditrigonal Icosidodecahedron
• Small Dodecacronic Hexecontahedron