Length of Segment AE in Triangle Arrangement

In triangle ABC, angle A measures $70^{ ext{o}}$. Point D is located on side BC such that the length of AD is extended to a point E, making $AD = DE$. If the triangle is inscribed in a circle with a radius of 10 units, what is the length of segment AE?

Recall that to apply the Law of Sines, we need to find the lengths of side AC and BC using properties of the triangle and the circle.