{"status": "success", "data": {"description_md": "In quadrilateral $ABCD$, $AB = 5$, $BC = 17$, $CD = 5$, $DA = 9$, and $BD$ is an integer. What is $BD$?\n\n<center><img class=\"problem-image\" alt='[asy] unitsize(4mm); defaultpen(linewidth(.8pt)+fontsize(8pt)); dotfactor=4;  pair C=(0,0), B=(17,0); pair D=intersectionpoints(Circle(C,5),Circle(B,13))[0]; pair A=intersectionpoints(Circle(D,9),Circle(B,5))[0]; pair[] dotted={A,B,C,D};  draw(D--A--B--C--D--B); dot(dotted); label(\"$D$\",D,NW); label(\"$C$\",C,W); label(\"$B$\",B,E); label(\"$A$\",A,NE); [/asy]' class=\"latexcenter\" height=\"85\" src=\"https://latex.artofproblemsolving.com/5/7/0/570b698fea7c6d66beab04dd6aee44dd24f2b6c1.png\" width=\"358\"/></center><br>\n\n$\\textbf{(A)}\\ 11 \\qquad \\textbf{(B)}\\ 12 \\qquad \\textbf{(C)}\\ 13 \\qquad \\textbf{(D)}\\ 14 \\qquad \\textbf{(E)}\\ 15$\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 quadrilateral <span class=\"katex--inline\">ABCD</span>, <span class=\"katex--inline\">AB = 5</span>, <span class=\"katex--inline\">BC = 17</span>, <span class=\"katex--inline\">CD = 5</span>, <span class=\"katex--inline\">DA = 9</span>, and <span class=\"katex--inline\">BD</span> is an integer. What is <span class=\"katex--inline\">BD</span>?</p>&#10;<center><img class=\"latexcenter\" alt=\"[asy] unitsize(4mm); defaultpen(linewidth(.8pt)+fontsize(8pt)); dotfactor=4;  pair C=(0,0), B=(17,0); pair D=intersectionpoints(Circle(C,5),Circle(B,13))[0]; pair A=intersectionpoints(Circle(D,9),Circle(B,5))[0]; pair[] dotted={A,B,C,D};  draw(D--A--B--C--D--B); dot(dotted); label(&#34;$D$&#34;,D,NW); label(&#34;$C$&#34;,C,W); label(&#34;$B$&#34;,B,E); label(&#34;$A$&#34;,A,NE); [/asy]\" height=\"85\" src=\"https://latex.artofproblemsolving.com/5/7/0/570b698fea7c6d66beab04dd6aee44dd24f2b6c1.png\" width=\"358\"/></center><br/>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 11 \\qquad \\textbf{(B)}\\ 12 \\qquad \\textbf{(C)}\\ 13 \\qquad \\textbf{(D)}\\ 14 \\qquad \\textbf{(E)}\\ 15</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": 2, "problem_name": "2009 AMC 12A Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12A_p11", "prev": "/problem/09_amc12A_p09"}}