# Putnam Problem of the Day (2)

#### simplependulum

MHF Hall of Honor
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 $$\displaystyle ABCD$$ .

Moderator edit: Approved Challenge question.

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