that's awesome. now i want to know how it's done.

9.78571?

I get the same answer with the link and confirm with separate calculation.

This can be solved by trig or geometry.

Geometry solution

The property of chords in a circle state

"

*Where two chords intersect, the product of the segment lengths of one chord must equal the product of the segment lengths of the other chord*"

A chord is any line drawn within a circle. In this case the chord will intersect at 90 deg.

One chord in this puzzle is 15 in long. The other chord would bisect this, so each segment is 7.5in long.

The other chord is ( 3.5in + a in) long which is the diameter.

Hence (7.5 * 7.5) = ( 3.5 x a).

Hence a = (7.5 * 7.5) / 3.5 = 16.0714 in

So diameter = 3.5 + 16.0714 = 19.5714 in

Radius = 19.5714 / 2 = 9.785714 in

Trig method is to use right angle triangles. I am not going to attempt to draw this one out.