2026 AIME I Problem 10

Let \triangle ABC have side lengths AB=13, BC=14, and CA=15. Triangle \triangle A'B'C' is obtained by rotating \triangle ABC about its circumcenter so that \overline{A'C'} is perpendicular to \overline{BC}, with A' and B not on the same side of line B'C'. Find the integer closest to the area of hexagon AA'CC'BB'.

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.