Finance puzzle

Here is the problem : 
Two random points, one red and one blue, are chosen uniformly and independently from the interior of a square. To ten decimal places1, what is the probability that there exists a point on the side of the square closest to the blue point that is equidistant to both the blue point and the red point?

 I obtained the following probability :
$P(0\le \frac{x_{r}^{2}+y_{r}^{2}-x_{b}^{2}-y_{b}^{2}}{-2y_{b}+2y_{r}} \le 1)$
with $x_{r}, y_{r}, x_{b}, y_{b}$ being the x-y coordinates of the red and blue point. I considered a 1x1 square, so thoses coordinates are between 0 and 1 (randomly). 
Can you help me solve this probability ?
Thank you ! :)