Circle

Let's set the center of the circle as O. 

Draw a line from O perpendicular to the chord. Let this line be OM. 

$OA = 15 \\ AM = AB / 2 = 4/2 = 2$

Triangle AOM is right, with angle AMO being 90 degrees.

By using the pythagorean theorem, we have

$OM = \sqrt{ OA^2 -AM^2} = \sqrt{ 15^2 - 2^2 } = \sqrt{221}$

So sqrt221 is our answer. 

Thanks! :)