AMO 2020 Problem 6

Let $ABCD$ be a square. For a point $P$ inside it, a windmill centred at $P$ consists of 2 perpendicular lines $l_1$ and $l_2$ passing through $P$ , such that $\bullet ~$ $l_1$ intersects the sides AB and CD at W and Y, respectively, and $\bullet ~$ $l_2$ intersects the side BC and DA at X and Z, respectively.

A windmill is called round if the quadrilateral WXYZ is cyclic. Determine all points P inside the square such that every windmill centred at P is round.