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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

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.

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: 2
config / split: default / train

Official source

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