A circle is circumscribed around triangle ABC centered at point O, and point O lies in the middle of side AB.

A circle is circumscribed around triangle ABC centered at point O, and point O lies in the middle of side AB. Find AC if AB = √47 and BC = √22.

Since the center of the circle lies in the middle of the side of the triangle, then this side is the diameter of the circle, the triangle is rectangular with the hypotenuse AB. Then, by the Pythagorean theorem, we obtain:
AC ^ 2 = AB ^ 2-BC ^ 2.
AC ^ 2 = (√47) ^ 2- (√22) ^ 2 = 47-22 = 25
AC = √25 = 5.