2017 AMC 12A Problem 24

Quadrilateral ABCD is inscribed in circle O and has side lengths AB=3, BC=2, CD=6, and DA=8. Let X and Y be points on \overline{BD} such that \frac{DX}{BD} = \frac{1}{4} and \frac{BY}{BD} = \frac{11}{36}. Let E be the intersection of line AX and the line through Y parallel to \overline{AD}. Let F be the intersection of line CX and the line through E parallel to \overline{AC}. Let G be the point on circle O other than C that lies on line CX. What is XF\cdot XG?

\textbf{(A) }17\qquad\textbf{(B) }\frac{59 - 5\sqrt{2}}{3}\qquad\textbf{(C) }\frac{91 - 12\sqrt{3}}{4}\qquad\textbf{(D) }\frac{67 - 10\sqrt{2}}{3}\qquad\textbf{(E) }18

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.