1993 AMC 12 Question 23

Question 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 $AX=$

1. $\cos6^\circ\cos12^\circ\sec18^\circ$
2. $\cos6^\circ\sin12^\circ\csc18^\circ$
3. $\cos6^\circ\sin12^\circ\sec18^\circ$
4. $\sin6^\circ\sin12^\circ\csc18^\circ$
5. $\sin6^\circ\sin12^\circ\sec18^\circ$