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) |

(5) |

**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.

© 1996-9

1999-05-26