Let $S$ be a square of side length $1$ . Two points are chosen at random on the sides of $S$ . The probability that the straight-line distance between the points is at least $\tfrac12$ is $\tfrac{a-b\pi}c$ , where $a$ , $b$ , and $c$ are positive integers with $\gcd(a,b,c)=1$ . What is $a+b+c$ ?