{"status": "success", "data": {"description_md": "In $\\triangle ABC$, we have $AB = 1$ and $AC = 2$. Side $\\overline{BC}$ and the median from $A$ to $\\overline{BC}$ have the same length. What is $BC$?\n\n$\\mathrm{(A)}\\ \\frac{1+\\sqrt{2}}{2}<br>\\qquad\\mathrm{(B)}\\ \\frac{1+\\sqrt{3}}2<br>\\qquad\\mathrm{(C)}\\ \\sqrt{2}<br>\\qquad\\mathrm{(D)}\\ \\frac 32<br>\\qquad\\mathrm{(E)}\\ \\sqrt{3}$\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> , we have  <span class=\"katex--inline\">AB = 1</span>  and  <span class=\"katex--inline\">AC = 2</span> . Side  <span class=\"katex--inline\">\\overline{BC}</span>  and the median from  <span class=\"katex--inline\">A</span>  to  <span class=\"katex--inline\">\\overline{BC}</span>  have the same length. What is  <span class=\"katex--inline\">BC</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac{1+\\sqrt{2}}{2}&lt;br&gt;\\qquad\\mathrm{(B)}\\ \\frac{1+\\sqrt{3}}2&lt;br&gt;\\qquad\\mathrm{(C)}\\ \\sqrt{2}&lt;br&gt;\\qquad\\mathrm{(D)}\\ \\frac 32&lt;br&gt;\\qquad\\mathrm{(E)}\\ \\sqrt{3}</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": "2002 AMC 12B Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12B_p24", "prev": "/problem/02_amc12B_p22"}}