AHSME 1993 Problem 23

Points $A,B,C$ and $D$ are on a circle of diameter $1$, and $X$ is on diameter $\overline{AD}.$ If $BX=CX$ and $3\angle{BAC}=\angle{BXC}=36^\circ$, then $AX=$

$\text{(A) } \cos(6^\circ)\cos(12^\circ)\sec(18^\circ) \\ \text{(B) } \cos(6^\circ)\sin(12^\circ)\csc(18^\circ) \\ \text{(C) } \cos(6^\circ)\sin(12^\circ)\sec(18^\circ) \\ \text{(D) } \sin(6^\circ)\sin(12^\circ)\csc(18^\circ) \\ \text{(E) } \sin(6^\circ)\sin(12^\circ)\sec(18^\circ)$