Let be a convex quadrilateral such that diagonals and intersect at right angles , and let be their intersection . Prove that the reflections of across are concyclic

Hint :

Consider the quadrilateral constructed by the feet of the perpendicular of\(\displaystyle E\) to the sides of \(\displaystyle ABCD\) .

Hint :

**Moderator edit:**Approved Challenge question.
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