Triangle A B C has A B=13, B C=14 and A C=15. Let P be the point on \overline{A C} such that P C=10. There are exactly two points D and E on line B P such that quadrilaterals A B C D and A B C E are trapezoids. What is the distance D E ?
Answer Choices
A. \dfrac{42}{5}
B. 6 \sqrt{2}
C. \dfrac{84}{5}
D. 12 \sqrt{2}
E. 18