Why is the midpoint half the hypotenuse of a triangle?

The circenter -------------In the special case of a right triangle, the circenter (C in the figure at right) lies exactly at the midpoint of the hypotenuse (longest side). a href="http://www.mathopenref.com/trianglecircenter.html" rel="nofollow"http://www.mathopenref.com/trianglecircu…/a In a right triangle, the circenter is the midpoint of the hypotenuse, since the hypotenuse will be a diameter of the circircle. a href="http://www-math.cudenver.edu/~wcherowi/courses/m3210/hgex2f06.html" rel="nofollow"http://www-math.cudenver.edu/~wcherowi/c…/a the center of the circle that cirscribes a right triangle is the midpoint of the hypotenuse and its radius is one half the length of the hypotenuse a href="http://en.wikipedia.org/wiki/Right_triangle" rel="nofollow"http://en.wikipedia.org/wiki/Right_trian…/a The distances between the midpoint of the hypotenuse and all three vertices are the same. In other words, the length of a hypotenuse median (see its definition below) is half of the hypotenuse length. a href="http://sakharov.net/triangle.html" rel="nofollow"http://sakharov.net/triangle.html/a