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I think the probability is zero because a circle doesn't have any edges

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    $\begingroup$ The edge is the circumference of the circle. If I were throwing the dart the probability would be zero because my darts would always be outside the circle. Here you are expected to assume the dart hits uniformly within the circle. $\endgroup$ – Ross Millikan Aug 12 at 4:43
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The region whose points are closer to the centre of a circle with radius $r$ than to the edge is easily seen to be another circle of radius $r/2$. Hence the desired probability is $\left(\frac12\right)^2=\frac14$.

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