Hypotenuse
From AoPSWiki
The hypotenuse of a right triangle is the side opposite the right angle. It is also the longest side of the triangle.
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 .
See also
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