Given a quadrilateral $ABCD$, inscribed in a circle $\omega$ such that $AB=AD$ and $CB=CD$ . Take the point $P \in \omega$. Let the vertices of the quadrilateral $Q_1Q_2Q_3Q_4$ be symmetric to the point P wrt the lines $AB$, $BC$, $CD$, and $DA$, respectively. a) Prove that the points symmetric to the point $P$ wrt lines $Q_1Q_22, Q_2Q_3, Q_3Q_4$ and $Q_4Q_1$, lie on one line. b) Prove that when the point $P$ moves in a circle $\omega$, then all such lines pass through one common point.