# 3 points in a circle

Geometry Level 4

Consider two points: $$A=(0,0)$$ which is the center of a unit circle, and $$B=(0,1)$$ which lies on that unit circle. Now, you choose a third point $$C$$ inside the circle uniformly at random.

What is the probability that you will be able to draw a square such that all three points $$A, B, C$$ lie on two adjacent sides of the square?