{"status": "success", "data": {"description_md": "In $\\triangle ABC$, $D$ is on $AC$ and $F$ is on $BC$. Also, $AB \\perp AC$, $AF \\perp BC$, and $BD = DC = FC = 1$. Find $AC$.\n\n<center><img class=\"problem-image\" src=\"/static/AHSME/1984/crops/84_ahsme_p27_fig.png\" alt=\"figure\" width=\"422\"></center>\n\n$\\text{(A)}\\ \\sqrt{2}\\qquad\\text{(B)}\\ \\sqrt{3}\\qquad\\text{(C)}\\ \\sqrt[3]{2}\\qquad\\text{(D)}\\ \\sqrt[3]{3}\\qquad\\text{(E)}\\ \\sqrt[4]{3}$\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>In <span class=\"katex--inline\">\\triangle ABC</span>, <span class=\"katex--inline\">D</span> is on <span class=\"katex--inline\">AC</span> and <span class=\"katex--inline\">F</span> is on <span class=\"katex--inline\">BC</span>. Also, <span class=\"katex--inline\">AB \\perp AC</span>, <span class=\"katex--inline\">AF \\perp BC</span>, and <span class=\"katex--inline\">BD = DC = FC = 1</span>. Find <span class=\"katex--inline\">AC</span>.</p>\n<center><img class=\"problem-image\" src=\"/static/AHSME/1984/crops/84_ahsme_p27_fig.png\" alt=\"figure\" width=\"422\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ \\sqrt{2}\\qquad\\text{(B)}\\ \\sqrt{3}\\qquad\\text{(C)}\\ \\sqrt[3]{2}\\qquad\\text{(D)}\\ \\sqrt[3]{3}\\qquad\\text{(E)}\\ \\sqrt[4]{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": 3, "problem_name": "1984 AHSME Problem 27", "can_next": true, "can_prev": true, "nxt": "/problem/84_ahsme_p28", "prev": "/problem/84_ahsme_p26"}}