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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