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AIME 2024 / AIME 2024 train ec2a3bb1-1f75-5e49-a899-725114f572d5

Problem

Answer published by the source. Consult the official source to check your work against its answer.

Problem

Let AA, BB, CC, and DD be points on the hyperbola x220−y224=1\frac{x^2}{20}- \frac{y^2}{24} = 1 such that ABCDABCD is a rhombus whose diagonals intersect at the origin. Find the greatest real number that is less than BD2BD^2 for all such rhombi.
Plain-text mathematical notation (without MathML)
Let A, B, C, and D be points on the hyperbola (x²)/(20)−(y²)/(24)=1 such that ABCD is a rhombus whose diagonals intersect at the origin. Find the greatest real number that is less than BD² for all such rhombi.
Original LaTeX notation
Let $A$, $B$, $C$, and $D$ be points on the hyperbola $\frac{x^2}{20}- \frac{y^2}{24} = 1$ 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.

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Source and history

task_id
ec2a3bb1-1f75-5e49-a899-725114f572d5
task_key
default--train--ec2a3bb1-1f75-5e49-a899-725114f572d5
task_revision_id
3
config / split
default / train

Official source

initial import