Altitude (triangle)#Orthic triangle

The Höhenfußpunktdreieck ( rare: orthisches triangle) is a term from the triangle geometry. It arises from the fact that the bases of the three heights (ie, the points and in which the solder of the cut corners of the triangle to the opposite sides of this site ) are joined together. In the special case of a right-angled triangle the Höhenfußpunktdreieck is degenerate, since then coincide two base points. The " Höhenfußpunktdreieck " is the orthocenter ( Ortho center ) associated Fußpunktdreieck.

Properties

• Each height of the original triangle bisects either an interior angle or an exterior angle of the Höhenfußpunktdreiecks. Therefore true for an acute triangle ABC the orthocenter H of the triangle with incenter of Höhenfußpunktdreiecks match. If the triangle ABC, however obtuse, so H is equal to one of the Ankreismittelpunkte Fußpunktdreiecks.
• The radius of the Höhenfußpunktdreiecks is the Feuerbach circle of the original triangle.
• Fagnano problem: Among all triangles that are inscribed in a acute triangle, the Höhenfußpunktdreieck has the smallest perimeter.