Intersecting Circles

Geometry Level 3

Circles Γ1 \Gamma_1 and Γ2\Gamma_2 have radii 1515 and 33 , respectively. They intersect at 22 distinct points AA and BB. A line l l through AA intersects Γ1 \Gamma_1 and Γ2\Gamma_2 at CC and DD, respectively. What is the value of BCBD \frac{BC}{BD} ?

Details and assumptions

Clarification: The line ll is not allowed to be ABAB, which would make B=C=DB=C=D which would cause the fraction to be meaningless.

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