Right triangle then with equality only in the isosceles case. If segments of lengths "p" and "q" emanating from vertex "C" trisect the hypotenuse into segments of length "c"/3, then The right triangle is the only triangle having two, rather than one or three, distinct inscribed squares. Let "h" and "k" ("h" > "k") be the sides of the two inscribed squares in a right triangle with hypotenuse "c". Then These sides and the incircle radius "r" are related by a similar formula: The perimeter of a right triangle equals the sum of the radii of the incircle and the three excircles:
Integer triangle "c" , "a" + "b" ≤ "c" and "a" ≤ "b" ≤ "c". This is also the number of integer sided obtuse or right (non-acute) triangles with largest side "c". The sequence starting at "c" = 1, is: Consequently, the difference between the two above sequences gives the number of acute integer sided triangles (up to congruence) with given largest side "c". The sequence starting at "c" = 1, is: By Heron's formula, if "T" is the area of a triangle whose sides have lengths "a", "b", and "c" then Since all the terms under the radical on the right