If the locus of the mid-point of the line segment from the point $( 3,2 )$ to a point on the circle, $x ^ { 2 } + y ^ { 2 } = 1$ is a circle of radius $r$, then $r$ is equal to\\
(1) $\frac { 1 } { 4 }$\\
(2) 1\\
(3) $\frac { 1 } { 3 }$\\
(4) $\frac { 1 } { 2 }$