In \triangle A B C, A B=13, B C=15, and C A=14. Point D is on \overline{B C} with C D=6. Point E is on \overline{B C} such that \angle B A E \cong \angle C A D. Given that B E=p / q, where p and q are relatively prime positive integers, find q.
In \triangle A B C, A B=13, B C=15, and C A=14. Point D is on \overline{B C} with C D=6. Point E is on \overline{B C} such that \angle B A E \cong \angle C A D. Given that B E=p / q, where p and q are relatively prime positive integers, find q.