1999 AIME Problem 4

The two squares shown share the same center O_{} and have sides of length 1. The length of \overline{AB} is 43/99 and the area of octagon ABCDEFGH is m/n, where m_{} and n_{} are relatively prime positive integers. Find m+n.

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.