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
Special right triangle Pell numbers 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378... .. The smallest Pythagorean triples resulting are: Alternatively, the same triangles can be derived from the square triangular numbers. The Kepler triangle is a right triangle whose sides are in a geometric progression. If the sides are formed from the geometric progression "a", "ar", "ar" then its common ratio "r" is given by "r" = where "φ" is the golden ratio. Its sides are therefore in the ratio . Thus, the shape of the Kepler triangle is uniquely determined (up to a scale factor) by the requirement that