Prove that the median of a right triangle drawn to the hypotenuse is equal to half the hypotenuse.

Let’s describe a circle around the triangle ABC. Angle ABC = 90, then the degree measure of the arc AC = 180, and then the chord AC is the diameter of the circumscribed circle and the hypotenuse of the triangle.

Let’s build the radius BО. AO = OC = OB = R.

AC = 2 * AO = 2 * BO.

Then OB = AC / 2, as required to prove