2007 iTest Problems/Problem 42

Problem

During a movie shoot, a stuntman jumps out of a plane and parachutes to safety within a $100$ foot by $100$ foot square field, which is entirely surrounded by a wooden fence. There is a flag pole in the middle of the square field. Assuming the stuntman is equally likely to land on any point in the field, the probability that he lands closer to the fence than to the flag pole can be written in simplest terms as $\dfrac{a-b\sqrt c}d$ , where all four variables are positive integers, $c$ is a multple of no perfect square greater than $1$ , a is coprime with $d$ , and $b$ is coprime with $d$ . Find the value of $a+b+c+d$ .

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2007 iTest Problems/Problem 42

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