## Pedal Triangle

Given a point , the pedal triangle of is the Triangle whose Vertices are the feet of the perpendiculars from to the side lines. The pedal triangle of a Triangle with Trilinear Coordinates and angles , , and has Vertices with Trilinear Coordinates
 (1) (2) (3)

The third pedal triangle is similar to the original one. This theorem can be generalized to: the th pedal -gon of any -gon is similar to the original one. It is also true that

 (4)

(Johnson 1929, pp. 135-136). The Area of the pedal triangle of a point is proportional to the Power of with respect to the Circumcircle,
 (5)

(Johnson 1929, pp. 139-141).

See also Antipedal Triangle, Fagnano's Problem, Pedal Circle, Pedal Line, Schwarz's Triangle Problem

References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 22-26, 1967.

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