Let's draw the situation presented in the problem:
In order to determine the radius of the circle that contains the bridge, we'll use the following formula:

where h is the height of the arc and w is its width.
This formula is derived from the intersecting chords theorem:

Since in our case a is half of the width of the arc and b its height:


dividing both sides by h:

since the diameter of the circle is b+c, or in this case h+c:

since the radius is half the diameter:

Now, let's plug the data we were given into this formula:


So the radius of the circle will be 21.6878 ft.