Right triangle two legs (the two sides that meet at a right angle). This can be stated in equation form as where "c" is the length of the hypotenuse, and "a" and "b" are the lengths of the remaining two sides. Pythagorean triples are integer values of "a, b, c" satisfying this equation. The radius of the incircle of a right triangle with legs "a" and "b" and hypotenuse "c" is The radius of the circumcircle is half the length of the hypotenuse, Thus the sum of the circumradius and the inradius is half the sum of the legs: One of the
Altitude (triangle) The orthocenter lies inside the triangle if and only if the triangle is acute (i.e. does not have an angle greater than or equal to a right angle). If one angle is a right angle, the orthocenter coincides with the vertex at the right angle. Let denote the vertices and also the angles of the triangle, and let be the side lengths. The orthocenter has trilinear coordinates formula_2 and barycentric coordinates Since barycentric coordinates are all positive for a point in a triangle's interior but at least one is negative for a point in the exterior, and two of the