{"status": "success", "data": {"description_md": "A regular hexagon with center at the origin in the complex plane has opposite pairs of sides one unit apart. One pair of sides is parallel to the imaginary axis. Let $R$ be the region outside the hexagon, and let $S=\\{\\frac{1}{z}|z\\in R\\}$. Then the area of $S$ has the form $a\\pi+\\sqrt{b}$, where $a$ and $b$ are positive integers. Find $a+b$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A regular hexagon with center at the origin in the complex plane has opposite pairs of sides one unit apart. One pair of sides is parallel to the imaginary axis. Let <span class=\"katex--inline\">R</span> be the region outside the hexagon, and let <span class=\"katex--inline\">S=\\{\\frac{1}{z}|z\\in R\\}</span>. Then the area of <span class=\"katex--inline\">S</span> has the form <span class=\"katex--inline\">a\\pi+\\sqrt{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are positive integers. Find <span class=\"katex--inline\">a+b</span>.</p>&#10;<hr/>&#10;<p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2008 AIME II Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/08_aime_II_p14", "prev": "/problem/08_aime_II_p12"}}