2024 AIME I Problem 9

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 largest number less than BD^2 for all rhombuses ABCD.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.