Thread: Putnam Problem of the Day (2)

1. Putnam Problem of the Day (2)

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 :

Spoiler:
Consider the quadrilateral constructed by the feet of the perpendicular of $E$ to the sides of $ABCD$ .

Moderator edit: Approved Challenge question.