Right triangle and "b" are the legs of the triangle. If the incircle is tangent to the hypotenuse AB at point P, then denoting the semi-perimeter as "s", we have and , and the area is given by This formula only applies to right triangles. If an altitude is drawn from the vertex with the right angle to the hypotenuse then the triangle is divided into two smaller triangles which are both similar to the original and therefore similar to each other. From this: In equations, where "a", "b", "c", "d", "e", "f" are as shown in the diagram. Thus Moreover, the
Fermat's right triangle theorem of a right triangle with square area. By dividing by any common factors, one can assume that this triangle is primitive and from the known form of all primitive Pythagorean triples, one can set formula_23, formula_24, and formula_25, by which the problem is transformed into finding relatively prime integers formula_26 and formula_27 (one of which is even) such that formula_28 is square. The four linear factors formula_26, formula_27, formula_31, and formula_32 are relatively prime and therefore must themselves be squares; let formula_33 and formula_34. Both formula_35 and formula_36 must be odd since exactly one of formula_26 or formula_27 is even