Question 25
A point $P$ is chosen at random inside square $ABCD.$ The probability that $AP$ is neither the shortest nor the longest side of $\triangle APB$ can be written as $\dfrac{a + b\pi - c\sqrt{d}}{e},$ where $a,$ $b,$ $c,$ $d,$ and $e$ are positive integers, $\gcd(a, b, c, e) = 1,$ and $d$ is not divisible by the square of a prime. What is $a + b + c + d + e?$