Let \triangle A B C have A B=15, A C=20, and B C=21. Suppose \omega is a circle passing through A that is tangent to segment B C. Let point D \neq A be the second intersection of A B with \omega, and let point E \neq A be the second intersection of A C with \omega. Suppose D E is parallel to B C. If D E=\frac{a}{b}, where a, b are relatively prime positive integers, find a+b.