A bridge over a river is supported by a single semicircular arch. The diameter of the semicircular arch where the bridge meets the river is 24 feet wide. The roadway is 4 feet above the center of the arch. What is the vertical distance between the roadway and the arch 6 feet from the center? (In the image, $A = 24$, $B = 4$, $C = 6$.)
The vertical distance is feet.

Hint: