{"status": "success", "data": {"description_md": "The area of $\\triangle$$EBD$ is one third of the area of $\\triangle$$ABC$. Segment $DE$ is perpendicular to segment $AB$. What is $BD$?\n\n<center>  \n<img class=\"problem-image\" height=\"152\" src=\"https://latex.artofproblemsolving.com/9/5/3/953e7cbe2b2ee84c7c3ff7f6c642569bc2483c4e.png\" width=\"275\"/>  \n</center><br>\n\n$\\textbf{(A)}\\ \\frac{4}{3} \\qquad\\textbf{(B)}\\ \\sqrt{5} \\qquad\\textbf{(C)}\\ \\frac{9}{4} \\qquad\\textbf{(D)}\\ \\frac{4\\sqrt{3}}{3} \\qquad\\textbf{(E)}\\ \\frac{5}{2}$\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>The area of <span class=\"katex--inline\">\\triangle</span><span class=\"katex--inline\">EBD</span> is one third of the area of <span class=\"katex--inline\">\\triangle</span><span class=\"katex--inline\">ABC</span>. Segment <span class=\"katex--inline\">DE</span> is perpendicular to segment <span class=\"katex--inline\">AB</span>. What is <span class=\"katex--inline\">BD</span>?</p>&#10;<center>  &#10;<img class=\"problem-image\" height=\"152\" src=\"https://latex.artofproblemsolving.com/9/5/3/953e7cbe2b2ee84c7c3ff7f6c642569bc2483c4e.png\" width=\"275\"/>  &#10;</center><br/>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{4}{3} \\qquad\\textbf{(B)}\\ \\sqrt{5} \\qquad\\textbf{(C)}\\ \\frac{9}{4} \\qquad\\textbf{(D)}\\ \\frac{4\\sqrt{3}}{3} \\qquad\\textbf{(E)}\\ \\frac{5}{2}</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2011 AMC 10B Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc10B_p10", "prev": "/problem/11_amc10B_p08"}}