I'd recommend getting out a separate piece of graphing paper (or use a graphing calculator such as
Desmos) and drawing the two circles yourself. For simplicity's sake, I drew the circles as: \(\left(x-1\right)^2+\left(y-1\right)^2=1\) and \(\left(x+1\right)^2+\left(y-1\right)^2=1\), respectively. These circles intersect at the point (0, 1).
Suppose the square had side length \(s\). Can you see why this means the lower-left corner is at \( \left(-\frac{s}{2}, 0 \right) \) and the lower-right corner is at \( \left(\frac{s}{2}, 0 \right) \)? And going one step further, the upper-left corner is at \( \left(-\frac{s}{2}, s \right) \) and the upper-right corner is at \( \left(\frac{s}{2}, s \right) \).
Next, can you see why, in order for your diagram to match the given one, the upper-right corner of the square must be on the right circle? What does it mean for a point to be on a circle? What technique(s) have you learned for this? When you work it through you'll be left with two possible solutions for \(s\), but you can reject one of them as obviously incorrect.
