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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) $\frac{1}{2}$
(3) $1$
(4) $\frac{1}{3}$
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