The pedal triangle of a triangle and point is the triangle whose vertices are the projections of a to the sides of the triangle. For instance, when is the orthocenter of the triangle, the pedal triangle is the orthic triangle; when the term is used without further qualification, this is often what is meant by "the" pedal triangle of .
Any pedal triangle satisfies
If lies on the circumcircle of the triangle, the pedal triangle becomes the Simson line with respect to . This is useful both for showing that lies on the circumcircle, and for showing three points are collinear.
The area of the pedal triangle is given by