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?

Please submit your answer to two decimal places.

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