Triangle A B C has an obtuse angle at \angle A. Points D and E are placed on \overline{B C} in the order B, D, E, C such that \angle B A D=\angle B C A and \angle C A E=\angle C B A. If A B=10, A C=11, and D E=4, compute B C.
Triangle A B C has an obtuse angle at \angle A. Points D and E are placed on \overline{B C} in the order B, D, E, C such that \angle B A D=\angle B C A and \angle C A E=\angle C B A. If A B=10, A C=11, and D E=4, compute B C.