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
Magic triangle (mathematics) for any order need to be checked for the magic property. Order-3 magic triangles are the simplest (except for trivial magic triangles of order 1). Magic triangle (mathematics) A magic triangle (also called a perimeter magic triangle) is an arrangement of the integers from 1 to on the sides of a triangle with the same number of integers on each side, called the "order" of the triangle, so that the sum of integers on each side is a constant, the magic sum of the triangle. Unlike magic squares, there are different magic sums for magic triangles of the same order.