A point is chosen at random from the interior of square ABCD. What is the probability that the point is closer to either A or C than it is to the midpoint of the diagonal connecting A and C.
My attempt at solving the problem follows.
Let be the length of a side of the square. Then, there are points inside of the square. Furthermore, the midpoint of the diagonal connecting A and C is at the point .
For my square, point A is at point and point C is at point . I found the distances between points A and C, point A and the midpoint, and point C and the midpoint. However, I don't think I am approaching the solution.