There are circles $\omega_1$ and $\omega_2$. They intersect in two points, one of which is the point $A$. Point $B$ lies on $\omega_1$ such that $AB$ is tangent to $\omega_2$. The tangent to $\omega_1$ at $B$ intersects $\omega_2$ at points $C$ and $D$, where $D$ is closer to $B$. The line $AD$ intersects $\omega_1$ again at $E$. Given that $BD = 3$ and $CD = 13$, find the ratio $\frac{EB}{ED}$.

Let's think step by step and output the final answer within \boxed{}.
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