Isosceles triangle the hypotenuse to the right-angled vertex) divides the right triangle into two isosceles triangles. This is because the midpoint of the hypotenuse is the center of the circumcircle of the right triangle, and each of the two triangles created by the partition has two equal radii as two of its sides. Similarly, an acute triangle can be partitioned into three isosceles triangles by segments from its circumcenter, but this method does not work for obtuse triangles, because the circumcenter lies outside the triangle. Generalizing the partition of an acute triangle, any cyclic polygon that contains the center of its circumscribed
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