{"status": "success", "data": {"description_md": "Triangle $ABC$ has $\\angle BAC = 60^{\\circ}$, $\\angle CBA \\leq 90^{\\circ}$, $BC=1$, and $AC \\geq AB$. Let $H$, $I$, and $O$ be the orthocenter, incenter, and circumcenter of $\\triangle ABC$, respectively. Assume that the area of pentagon $BCOIH$ is the maximum possible. What is $\\angle CBA$?\n\n$\\textbf{(A)}\\ 60^{\\circ} \\qquad<br>\\textbf{(B)}\\ 72^{\\circ} \\qquad<br>\\textbf{(C)}\\ 75^{\\circ} \\qquad<br>\\textbf{(D)}\\ 80^{\\circ} \\qquad<br>\\textbf{(E)}\\ 90^{\\circ}$\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>Triangle  <span class=\"katex--inline\">ABC</span>  has  <span class=\"katex--inline\">\\angle BAC = 60^{\\circ}</span> ,  <span class=\"katex--inline\">\\angle CBA \\leq 90^{\\circ}</span> ,  <span class=\"katex--inline\">BC=1</span> , and  <span class=\"katex--inline\">AC \\geq AB</span> . Let  <span class=\"katex--inline\">H</span> ,  <span class=\"katex--inline\">I</span> , and  <span class=\"katex--inline\">O</span>  be the orthocenter, incenter, and circumcenter of  <span class=\"katex--inline\">\\triangle ABC</span> , respectively. Assume that the area of pentagon  <span class=\"katex--inline\">BCOIH</span>  is the maximum possible. What is  <span class=\"katex--inline\">\\angle CBA</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 60^{\\circ} \\qquad\\textbf{(B)}\\ 72^{\\circ} \\qquad\\textbf{(C)}\\ 75^{\\circ} \\qquad\\textbf{(D)}\\ 80^{\\circ} \\qquad\\textbf{(E)}\\ 90^{\\circ}</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": "2011 AMC 12A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/11_amc12A_p24"}}