Intersecting Circles

Geometry Level 3

Circles $\Gamma_1$ and $\Gamma_2$ have radii $15$ and $3$ , respectively. They intersect at $2$ distinct points $A$ and $B$ . A line $l$ through $A$ intersects $\Gamma_1$ and $\Gamma_2$ at $C$ and $D$ , respectively. What is the value of $\frac{BC}{BD}$ ?

Details and assumptions

Clarification: The line $l$ is not allowed to be $AB$ , which would make $B=C=D$ which would cause the fraction to be meaningless.