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
Heronian triangle triangles with these sidelengths, and joins them together along the sides of length "a", to obtain a triangle with integer side lengths "c", "e", and "b" + "d", and with area If "a" is even then the area "A" is an integer. Less obviously, if "a" is odd then "A" is still an integer, as "b" and "d" must both be even, making "b"+"d" even too. Some Heronian triangles cannot be obtained by joining together two right-angled triangles with integer sides as described above. For example, a 5, 29, 30 Heronian triangle with area 72 cannot be constructed from two