5.2.4.39 Various problems on the plane

Condition: In a convex quadrilateral \( A B C D \) the diagonals are mutually perpendicular and intersect at the point \( E \). Let \( A^{\prime}, B^{\prime}, C^{\prime}, D^{\prime}- \) points be symmetrical \( E \) with respect to the lines \( A B, B C, C D, D A \) respectively. Prove that the quadrilateral \( A^{\prime}, B^{\prime}, C^{\prime}, D^{\prime}- \) is cyclic.