1989 Putnam B1

A dart, thrown at random, hits a square target. Assuming that any two

parts of the target of equal area are equally likely to be hit, find

the probability that the point hit is nearer to the center than to any

edge. Express your answer in the form $\displaystyle{\frac{a\sqrt{b} + c}{d}}$,

where $a,\,b,\,c,\,d$ are integers.

随机投掷的飞镖击中方形目标。假设任意两个

相同面积的目标部分被击中的可能性相同，找到

击中点比任何击中点更接近中心的概率

边缘。以 $\displaystyle{\frac{a\sqrt{b} + c}{d}}$ 的形式表达你的答案，

其中 $a,\,b,\,c,\,d$ 是整数。