There are four points $A$, $B$, $C$, $D$ on a straight line, $AB: BC: CD=2: 1: 3$. Circles $\odot O_{1}$ and $\odot O_{2}$ are constructed with $AC$ and $BD$ as diameters, respectively. The two circles intersect at $E$ and $F$. Find $ED: EA$.
(1996, Huanggang Region, Hubei Province, Junior High School Mathematics Competition)