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
Incircle and excircles of a triangle has area formula_39. Similarly, formula_40 has area formula_41 and formula_42 has area formula_43. Since these three triangles decompose formula_35, we see that the area formula_45 is: where formula_48 is the area of formula_35 and formula_50 is its semiperimeter. For an alternative formula, consider formula_51. This is a right-angled triangle with one side equal to "r" and the other side equal to formula_52. The same is true for formula_53. The large triangle is composed of 6 such triangles and the total area is: The Gergonne triangle (of "ABC") is defined by the 3 touchpoints of the incircle on the 3 sides.