AMC 8 1996 Problem 25

A point is chosen at random from within a circular region. What is the probability that the point is closer to the center of the region than it is to the boundary of the region? $\text{(A)}\frac{1}{4} \text{(B)}\frac{1}{3} \text{(C)}\frac{1}{2} \text{(D)}\frac{2}{3} \text{(E)}\frac{3}{4}$