CMO 1986 Problem 1

In the diagram line segments $AB$ and $CD$ are of length 1 while angles $ABC$ and $CBD$ are $90^\circ$ and $30^\circ$ respectively. Find $AC$ .

import geometry;
import graph;

unitsize(1.5 cm);

pair A, B, C, D;

B = (0,0);
D = (3,0);
A = 2*dir(120);
C = extension(B,dir(30),A,D);

draw(A--B--D--cycle);
draw(B--C);
draw(arc(B,0.5,0,30));

label(" $A$ ", A, NW);
label(" $B$ ", B, SW);
label(" $C$ ", C, NE);
label(" $D$ ", D, SE);
label(" $30^\circ$ ", (0.8,0.2));
label(" $90^\circ$ ", (0.1,0.5));

perpendicular(B,NE,C-B);