Triangle A B C with A B=50 and A C=10 has area 120 . Let D be the midpoint of \overline{A B}, and let E be the midpoint of \overline{A C}. The angle bisector of \angle B A C intersects \overline{D E} and \overline{B C} at F and G, respectively. What is the area of quadrilateral F D B G ?
Answer Choices
A. 60
B. 65
C. 70
D. 75
E. 80