Difference between revisions of "2024 AIME I Problems/Problem 9"
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| + | ==Problem== | ||
| + | Let <math>A</math>, <math>B</math>, <math>C</math>, and <math>D</math> be point on the hyperbola <math>\frac{x^2}{20}- \frac{y^2}{24} = 1</math> such that <math>ABCD</math> is a rhombus whose diagonals intersect at the origin. Find the greatest real number that is less than <math>BD^2</math> for all such rhombi. | ||
| + | |||
| + | ==See also== | ||
| + | {{AIME box|year=2024|n=I|num-b=6|num-a=8}} | ||
| + | |||
| + | {{MAA Notice}} | ||
Revision as of 14:02, 2 February 2024
Problem
Let 
, 
, 
, and 
be point on the hyperbola 
such that 
is a rhombus whose diagonals intersect at the origin. Find the greatest real number that is less than 
for all such rhombi.
See also
| 2024 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
