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 \(m+n.\)

(第十七届AIME1999 第4题)