Let \(ABCD\) be a square, a point
\(I\) a random point on the plane.
Consider the four points, symmetric to \(I\) with respect to the midpoints of \(AB, BC, CD, AD\). Prove that these new four
points are vertices of a square.
In case you need a refresher, we say that a point \(X'\) is symmetric to a point \(X\) with respect to a point \(M\) if \(M\) is the midpoint of the segment \(XX'\).