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Found problems: 1

2024 AIME, 9
Tags: AMC , AIME , AIME I , asymptotes
Let $A$, $B$, $C$, and $D$ be points in the coordinate plane on the hyperbola $\tfrac{x^{2}}{20}-\tfrac{y^{2}}{24}=1$ such that $ABCD$ is a rhombus whose diagonals intersect at the origin. Find the greatest real number that is less than $BD^{2}$ for all such rhombi.