Right triangle angle vertex to the midpoint of the hypotenuse. Also, the center of the circle that circumscribes a right triangle is the midpoint of the hypotenuse and its radius is one half the length of the hypotenuse. The following formulas hold for the medians of a right triangle: The median on the hypotenuse of a right triangle divides the triangle into two isosceles triangles, because the median equals one-half the hypotenuse. The medians "m" and "m" from the legs satisfy In a right triangle, the Euler line contains the median on the hypotenuse—that is, it goes through both the right-angled vertex
Automedian triangle much more recent. The problem of characterizing automedian triangles was posed in the late 19th century in the "Educational Times" (in French) by Joseph Jean Baptiste Neuberg, and solved there with the formula 2"a" = "b" + "c" by William John Greenstreet. Apart from the trivial cases of equilateral triangles, the triangle with side lengths 17, 13, and 7 is the smallest (by area or perimeter) automedian triangle with integer side lengths. There is only one automedian right triangle, the triangle with side lengths proportional to 1, , and . This triangle is the second triangle in the spiral of