CheeseSteak1432

I actually found another solution on the website I got the problem from. Before I noticed that if two points are chosen that are at most a distance of 1 unit apart from each other, the angle that they make with the center point of the circle is at most 60 degrees (equilateral triangle). When I looked at the solution, I realized that that idea was actually a part of the solution. Let's say A is on the right side of the circle. That means point B could be chosen either above or below point A. This creates an arc of 120 degrees, and since there are 360 degrees in a circle, the correct solution is 120/360 = 1/3. Thank you all for giving your ideas!

Thank you for spending a long time on this explanation, but I am confused on how you found the bricked area. I see that you found the area of the sector, but what about the bricked area to the right of line segment DE?

Thanks for taking the time to answer my question, but I am slightly confused about the second parargaph. Firstly, did you mean that we should assume that A is located at (0, 1) instead of (1, 0) (this is assuming that the center of the circle is located at (0, 0))? Secondly, why don't we also consider the left side?

Thank you for your time and effort, but the website says that this is incorrect. 

I have come up with the thought that if two points are chosen that are at most a distance of 1 unit apart from each other, the angle that they make with the center point of the circle is at most 60 degrees (equilateral triangle). This thought might be incorrect, but if it is correct it might have something to do with the answer.