Pedal triangle

Fußpunktdreieck is a term from the triangle geometry. Are a triangle ABC and a point P where, the Fußpunktdreieck of P is given by the base points of the three alloys of P on the triangle sides. If P is on the circumcircle of ABC, the Fußpunktdreieck degenerates into a straight line, the line between so-called simson.

If the given point P is the orthocenter of the triangle, we use the term Höhenfußpunktdreieck.

The side lengths can be produced from a Fußpunktdreiecks the side lengths of the original triangle, calculating the distances from the corners to the point P and the radius r of the circumference. The following applies:

These relationships are also valid in the case of the degenerate triangle if P lies on the circumcircle and the corresponding sections on the simson between straights.