Quadrilateral A B C D is inscribed in circle O and has sides A B=3, B C=2, C D=6, and D A=8. Let X and Y be points on \overline{B D} such that
\dfrac{D X}{B D}=\dfrac{1}{4} \quad \text { and } \quad \dfrac{B Y}{B D}=\dfrac{11}{36}
Let E be the intersection of line A X and the line through Y parallel to \overline{A D}. Let F be the intersection of line C X and the line through E parallel to \overline{A C}. Let G be the point on circle O other than C that lies on line C X. What is X F \cdot X G ?
Answer Choices
A. 17
B. \dfrac{59-5 \sqrt{2}}{3}
C. \dfrac{91-12 \sqrt{3}}{4}
D. \dfrac{67-10 \sqrt{2}}{3}
E. 18