Hypotenuse

The hypotenuse of a right triangle is the side opposite the right angle. It is also the longest side of the 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 $\triangle ABC$ from $C$ is the same as $\frac12 AB$ , then $\triangle ABC$ is a right triangle with its right angle at $C$ .