Circumscribable Quadrilateral and Finding Lengths

In the attached figure, the quadrilateral ABCD has the following lengths of sides and diagonals:  DC=7, CB=8, BA=13, AD=13, AC=15, and BD=13.
1.  Verify that quadrilateral ABCD is circumscribable
2.  Find the remaining lengths of DE, BE, AE, and CE.

Although it appears there is a right angle, it is not labeled as though it is, so treat it like there is not a right angle.

Attached file(s):

Quadrilateral problem.jpg  View File