{"status": "success", "data": {"description_md": "Triangle $ABC$ has $\\angle C = 60^{\\circ}$ and $BC = 4$.  Point $D$ is the midpoint of $BC$.  What is the largest possible value of $\\tan{\\angle BAD}$?\n\n$\\mathrm{(A)}\\ \\frac{\\sqrt{3}}{6}\\qquad\\mathrm{(B)}\\ \\frac{\\sqrt{3}}{3}\\qquad\\mathrm{(C)}\\ \\frac{\\sqrt{3}}{2\\sqrt{2}}\\qquad\\mathrm{(D)}\\ \\frac{\\sqrt{3}}{4\\sqrt{2}-3}\\qquad\\mathrm{(E)}\\ 1$\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 C = 60^{\\circ}</span>  and  <span class=\"katex--inline\">BC = 4</span> .  Point  <span class=\"katex--inline\">D</span>  is the midpoint of  <span class=\"katex--inline\">BC</span> .  What is the largest possible value of  <span class=\"katex--inline\">\\tan{\\angle BAD}</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac{\\sqrt{3}}{6}\\qquad\\mathrm{(B)}\\ \\frac{\\sqrt{3}}{3}\\qquad\\mathrm{(C)}\\ \\frac{\\sqrt{3}}{2\\sqrt{2}}\\qquad\\mathrm{(D)}\\ \\frac{\\sqrt{3}}{4\\sqrt{2}-3}\\qquad\\mathrm{(E)}\\ 1</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": "2008 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12A_p25", "prev": "/problem/08_amc12A_p23"}}