Find the ratio of diagonals in Trapezoid 
Given $ABCD$ a rectangular trapezoid, $\angle A=90^\circ$, $AB\parallel DC$, $2AB = CD$ and $AC \perp BD$.
  What is the value of $AC/BD$ ?

Attempts so far:
I have tried using the ratio of the areas of triangles $AOB$ and $DOC$, which is $\frac14$ (where $O$ is the intersection of the diagonals), but I couldn't get anything useful. I don't know how to use the fact that the diagonals are perpendicular.

Put $AB=1$, $DC=2$, $AD=x$, and set the trapezoid with $A$ in the origin of a cartesian plane. Take the vector $AC=(x,2)$ and the vector $DB=(-x,1)$ and impose that they be orthogonal, i.e. their dot product be null, i.e. $x^2=2$. Now you have all the data to continue. 
