A machine-shop cutting tool has the shape of a notched circle, as shown. The radius of the circle is \sqrt{50} \mathrm{~cm}, the length of A B is 6 \mathrm{~cm} and that of B C is 2 \mathrm{~cm}. The angle A B C is a right angle. Find the square of the distance (in centimeters) from B to the center of the circle.
