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I was thinking about the above problem .Can someone point me in the right direction? Thanks in advance for your time.

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up vote 1 down vote accepted

For any point $A$ on the circle, $B$ will be any point on the circle of radius $b$ with center $A$. Since this will be true for any $A$ on the circle, the locus of $B$ will be the figure formed by a circle that rotates around a point. Therefore, I would say the right answer is C, since for any point in the region between the two cocentric circles you can find an $A$ such that $A$ is on the circle and $|AB|=b$.

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This is a right picture of what is going on the plane. – Babak S. Jan 15 '13 at 16:23

The locus of B takes every point on the circle to another, some distance $b$ from the original in a given direction. Does that help?

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A is on the circumference of the circle. – Daniel Littlewood Jan 15 '13 at 16:02
    
On the circle means on the circumference of the circle..that is what i think from the question.No other information is given about it. – user52976 Jan 15 '13 at 16:02

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