On a line $r$, points $A$ and $B$ are marked, and on a line $s$, parallel to $r$, points $C$ and $D$ are marked, such that $A B C D$ is a square. Point $E$ is also marked on the segment $C D$.
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a) What is the ratio between the areas of triangles $A B E$ and $B C D$, if $E$ is the midpoint of $C D$?

b) What is the ratio $\frac{D E}{E C}$, so that the area of triangle $B F E$ is double the area of $D F E$, where $F$ is the intersection of segments $A E$ and $B D$?