By the Pythagorean theorem, the length of the hypotenuse of a triangle with legs of length and is .
For any right triangle, the hypotenuse is a diameter of the circumcircle. It follows that the midpoint of the hypotenuse of the triangle is the center of the circle. The converse also holds: if the length of the median of from is the same as , then is a right triangle with its right angle at .
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