Answer
3
Work Step by Step
We find the radius of the circumscribed circle, which is the hypotenuse of the right triangle:
$$ =\sqrt{6^2+8^2} \\ =10$$
We know the following equations:
$$ a+b-2r=2R$$
Where a and b are the legs, R is the radius of the circumscribed circle, and r is the radius of the inscribed circle. Plugging in known values, we find:
$$ 6+8-2r=(2)(10) \\ 14+2r=20 \\ 2r =6 \\ r=3$$
