{"status": "success", "data": {"description_md": "Figure $ABCD$ is a trapezoid with $AB \\| DC$, $AB = 5$, $BC = 3\\sqrt{2}$, $\\angle BCD = 45^\\circ$ and $\\angle CDA = 60^\\circ$. The length of $DC$ is\n\n<center><img class=\"problem-image\" src=\"/static/AHSME/1984/crops/84_ahsme_p08_fig.png\" alt=\"figure\" width=\"480\"></center>\n\n$\\text{(A)}\\ 7 + \\frac{2}{3}\\sqrt{3}\\qquad\\text{(B)}\\ 8\\qquad\\text{(C)}\\ 9\\frac{1}{2}\\qquad\\text{(D)}\\ 8 + \\sqrt{3}\\qquad\\text{(E)}\\ 8 + 3\\sqrt{3}$\n\n___\n\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.\n", "description_html": "<p>Figure <span class=\"katex--inline\">ABCD</span> is a trapezoid with <span class=\"katex--inline\">AB \\| DC</span>, <span class=\"katex--inline\">AB = 5</span>, <span class=\"katex--inline\">BC = 3\\sqrt{2}</span>, <span class=\"katex--inline\">\\angle BCD = 45^\\circ</span> and <span class=\"katex--inline\">\\angle CDA = 60^\\circ</span>. The length of <span class=\"katex--inline\">DC</span> is</p>\n<center><img class=\"problem-image\" src=\"/static/AHSME/1984/crops/84_ahsme_p08_fig.png\" alt=\"figure\" width=\"480\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 7 + \\frac{2}{3}\\sqrt{3}\\qquad\\text{(B)}\\ 8\\qquad\\text{(C)}\\ 9\\frac{1}{2}\\qquad\\text{(D)}\\ 8 + \\sqrt{3}\\qquad\\text{(E)}\\ 8 + 3\\sqrt{3}</span></p>\n<hr>\n<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>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "1984 AHSME Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/84_ahsme_p09", "prev": "/problem/84_ahsme_p07"}}