KöMaL 2022 C1731

The parallel sides of a trapezium $ABCD$ are $AB>CD$. The midline of the trapezium intersects diagonal $AC$ at $E$ and diagonal $BD$ at $F$. The length of line segment $CD$ is the $a)$ arithmetic $b)$ geometric mean of line segments $AB$ and $EF$. In which of the two cases will the ratio $\dfrac{AB}{CD}$ have a larger value?