Pedal triangle

Let the triangle be ABC, and the point P. Drop perpendiculars from P to the three sides of the triangle (these may need to be produced, ie extended). Label L, M, N the intersections of the lines from P with the sides BC, AC, AB. The pedal triangle is then LMN.

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

If P is on the circumcircle of the triangle, LMN collapses to a line. This is then called the pedal line, or sometimes the Simson line after Robert Simson.

External Link

• http://mathworld.wolfram.com/PedalTriangle
• Java applet showing the perpendiculars: http://s13a.math.aca.mmu.ac.uk/Geometry/TGeomUnit/TriGeom2