Let A B C D be a convex quadrilateral with A B=2, A D=7, and C D=3 such that the bisectors of acute angles \angle D A B and \angle A D C intersect at the midpoint of \small\overline{B C}. Find the square of the area of A B C D.
Let A B C D be a convex quadrilateral with A B=2, A D=7, and C D=3 such that the bisectors of acute angles \angle D A B and \angle A D C intersect at the midpoint of \small\overline{B C}. Find the square of the area of A B C D.