Question 88
Let $ABCDEF$ be a hexagon with $\angle BAF = 150^\circ$, $\angle ACB = \angle ADC = 90^\circ$ and $|AC| = |BC|$. Assume also that the triangle $ABC$ is similar to the triangle $ADE$ and the triangle $BCD$ is similar to the triangle $DEF$. Find the ratio of the lengths of the segments $AB$ and $AF$.