A2. The center of a circle with radius 1 coincides with the intersection of the diagonals of a square.

The circle and the square have the same

![](https://cdn.mathpix.com/cropped/2024_04_17_9dc9851d634283e8a951g-1.jpg?height=340&width=323&top_left_y=1640&top_left_x=1546)
area. The circle intersects a side of the square at points $A$ and $B$.

How long is the line segment $A B$?