Given that radius of the sphere(AB) =  15 units.

radius of the circle(BC) =  10 units.

Use the Pythagorean Theorem for right triangle ACB to solve for AC.

                 (Pythagorean theorem)

                  (Substitute )

                        (Evaluate powers)

   (Subtract 100 from each side)

                        (Simplify)

                                  (Subtract: )

                                     (Taking out square root)

The value of AC is approximately 11.1 units.