{"status": "success", "data": {"description_md": "In $\\triangle{ABC}$ with side lengths $AB = 13$, $AC = 12$, and $BC = 5$, let $O$ and $I$ denote the circumcenter and incenter, respectively. A circle with center $M$ is tangent to the legs $AC$ and $BC$ and to the circumcircle of $\\triangle{ABC}$. What is the area of $\\triangle{MOI}$?\n\n$\\textbf{(A)}\\ \\frac52\\qquad\\textbf{(B)}\\ \\frac{11}{4}\\qquad\\textbf{(C)}\\ 3\\qquad\\textbf{(D)}\\ \\frac{13}{4}\\qquad\\textbf{(E)}\\ \\frac72$\n___\nFull 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  <span class=\"katex--inline\">\\triangle{ABC}</span>  with side lengths  <span class=\"katex--inline\">AB = 13</span> ,  <span class=\"katex--inline\">AC = 12</span> , and  <span class=\"katex--inline\">BC = 5</span> , let  <span class=\"katex--inline\">O</span>  and  <span class=\"katex--inline\">I</span>  denote the circumcenter and incenter, respectively. A circle with center  <span class=\"katex--inline\">M</span>  is tangent to the legs  <span class=\"katex--inline\">AC</span>  and  <span class=\"katex--inline\">BC</span>  and to the circumcircle of  <span class=\"katex--inline\">\\triangle{ABC}</span> . What is the area of  <span class=\"katex--inline\">\\triangle{MOI}</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac52\\qquad\\textbf{(B)}\\ \\frac{11}{4}\\qquad\\textbf{(C)}\\ 3\\qquad\\textbf{(D)}\\ \\frac{13}{4}\\qquad\\textbf{(E)}\\ \\frac72</span> </p>&#10;<hr><p>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": 5, "problem_name": "2018 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12B_p22", "prev": "/problem/18_amc12B_p20"}}