Beside the Point

November 2024 : Puzzle

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?

  1. (Or, if you want to send in the exact answer, that’s fine too!)