hypotenuse

Let $ABC$ a right triangle in a Euclidean geometry with right angle at $C$. Then $AB$ is called the hypotenuse of $ABC$.

The midpoint $P$ of the hypotenuse coincides with the circumcenter of the triangle, so it is equidistant from the three vertices. When the triangle is inscribed on his circumcircle, the hypotenuse becomes a diameter. So the distance from $P$ to the vertices is precisely the circumradius.

The hypotenuse’s length can be calculated by means of the Pythagorean theorem:

$$c=\sqrt{a^2+b^2}$$