# 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.

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