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)