Answer
$\sqrt{5}$
Work Step by Step
We know that the center of the circumscribed circle is the midpoint of the line BA. Assuming that point C of the triangle is the origin, this means that the midpoint is (4,3). We now consider the midpoint of the inscribed circle, which is given by:
$r =\frac{ab}{a+b+c} \\ r = \frac{8\times 6}{8+6+10} = 2$
Thus, we use the distance formula to find the distance:
$ d = \sqrt{(4-2)^2 + (3-2)^2} = \sqrt{5}$
