If the locus of the mid-point of the line segment from the point \( (3,2) \) to a point on a cir...

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