The two squares shown share the same center O and have sides of length 1. The length of \overline{A B} is 43 / 99 and the area of octagon A B C D E F G H is m / n, where m and n are relatively prime positive integers. Find m+n.

The two squares shown share the same center O and have sides of length 1. The length of \overline{A B} is 43 / 99 and the area of octagon A B C D E F G H is m / n, where m and n are relatively prime positive integers. Find m+n.