2026 AIME II Problem 10

Let \triangle ABC{} be a triangle with D on \overline{BC} such that \overline{AD}{} bisects \angle BAC. Let \omega{} be the circle that passes through A and is tangent to segment \overline{BC}{} at D. Let E \neq A and F \neq A be the intersections of \omega{} with segments \overline{AB}{} and \overline{AC}, respectively. Suppose that AB = 200, AC = 225, and all of AE, AF, BD, and CD{} are positive integers. Find the greatest possible value of BC.

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.