问题316: Suppose in triangle ABC that the angle at A is greater than

Suppose in triangle ABC that the angle at A is greater than a right angle. Points
D and E are placed on the side BC such that B, D, E, C lie on the side in that
order, and ∠BAD = ∠BCA and ∠CAE = ∠CBA. Given that AB = 10, AC = 11
and DE = 4, find the length BC.