Carnot's theorem

The set of Carnot ( Lazare Nicholas Marguerite Carnot after ) describes in any triangle relationship between Inkreisradius, circumradius and the distances of the radius center point of the triangle sides. He states that the sum of the signed distances is equal to the sum of Inkreisradius and radius radius.

Herein, the radius of the circumference with a center and the radius of the inscribed circle with the center of a triangle. The points are the base points of the solders of the triangle sides. The function returns the length of a line if it extends entirely or partially in the interior of the triangle, and the length of negative if it is located completely outside of the triangle.

In the special case of the acute angle of the right triangle and the signed distances are all negative, so that you simply can not use the sum of all distances in this case.