{"status": "success", "data": {"description_md": "In equiangular octagon $CAROLINE$, $CA = RO = LI = NE = \\sqrt{2}$ and $AR = OL = IN = EC = 1$. The self-intersecting octagon $CORNELIA$ encloses six non-overlapping triangular regions. Let $K$ be the area enclosed by $CORNELIA$, that is, that total area of the six triangular regions. Then $K=\\tfrac{a}{b}$ where $a$ and $b$ are relatively prime 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>In equiangular octagon <span class=\"katex--inline\">CAROLINE</span>, <span class=\"katex--inline\">CA = RO = LI = NE = \\sqrt{2}</span> and <span class=\"katex--inline\">AR = OL = IN = EC = 1</span>. The self-intersecting octagon <span class=\"katex--inline\">CORNELIA</span> encloses six non-overlapping triangular regions. Let <span class=\"katex--inline\">K</span> be the area enclosed by <span class=\"katex--inline\">CORNELIA</span>, that is, that total area of the six triangular regions. Then <span class=\"katex--inline\">K=\\tfrac{a}{b}</span> where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are relatively prime positive integers. Find <span class=\"katex--inline\">a + b</span>.</p>&#10;<hr><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>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2018 AIME II Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/18_aime_II_p05", "prev": "/problem/18_aime_II_p03"}}