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
Automedian triangle satisfying the formula "a" = "b" + "c". That is, in order for the three numbers "a", "b", and "c" to be the sides of an automedian triangle, the sequence of three squared side lengths "b", "a", and "c" should form an arithmetic progression. If "x", "y", and "z" are the three sides of a right triangle, sorted in increasing order by size, and if 2"x" < "z", then "z", "x" + "y", and "y" − "x" are the three sides of an automedian triangle. For instance, the right triangle with side lengths 5, 12, and 13 can be used