In geometry, a pedal triangle is obtained by projecting a point onto the sides of a triangle.

More specifically, consider a triangle ABC, and a point P that is not one of the vertices A, B, C. Drop perpendiculars from P to the three sides of the triangle (these may need to be produced, i.e., extended). Label L, M, N the intersections of the lines from P with the sides BC, AC, AB. The pedal triangle is then LMN.

If ABC is not an obtuse triangle, P is the orthocenter then the angles of LMN are 180°−2A, 180°−2B and 180°−2C.

The location of the chosen point P relative to the chosen triangle ABC gives rise to some special cases:

• If P = orthocenter, then LMN = orthic triangle.

• If P = incenter, then LMN = intouch triangle.

• If P = circumcenter, then LMN = medial triangle.

The case when P is on the circumcircle, and the pedal triangle degenerates into a line (red).