Question 133
A parallelogram $ABCD$ with $AC \gt BD$ is given. Let $k_1$ be the circle with diameter $AC$ and $k_2$ the circle with diameter $DC$. $k_1$ meets line $AB$ at the point $E$, $k_2$ meets the line $AC$ at the points $C$ and $O$, and line $AD$ at the point $F$. Suppose that $AO = a$, $FO = b$ and $\angle BAC = 45^\circ$. Find the ratio of the areas of the triangles $AOE$ and $COF$.