{"status": "success", "data": {"description_md": "In the five-sided star shown, the letters $A$, $B$, $C$, $D$ and $E$ are replaced by the<br>numbers 3, 5, 6, 7 and 9, although not necessarily in that order. The sums of the<br>numbers at the ends of the line segments $\\overline{AB}$, $\\overline{BC}$, $\\overline{CD}$, $\\overline{DE}$, and $\\overline{EA}$ form an<br>arithmetic sequence, although not necessarily in that order. What is the middle<br>term of the arithmetic sequence?<br><center><img class=\"problem-image\" alt='[asy] draw((0,0)--(0.5,1.54)--(1,0)--(-0.31,0.95)--(1.31,0.95)--cycle); label(\"$A$\",(0.5,1.54),N); label(\"$B$\",(1,0),SE); label(\"$C$\",(-0.31,0.95),W); label(\"$D$\",(1.31,0.95),E); label(\"$E$\",(0,0),SW); [/asy]' class=\"latexcenter\" height=\"235\" src=\"https://latex.artofproblemsolving.com/b/7/4/b742a9eaa62d04f46229732736080eeb97f05475.png\" width=\"252\"/></center>\n\n$(\\mathrm {A}) \\ 9 \\qquad (\\mathrm {B}) \\ 10 \\qquad (\\mathrm {C})\\ 11 \\qquad (\\mathrm {D}) \\ 12 \\qquad (\\mathrm {E})\\ 13$\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 the five-sided star shown, the letters  <span class=\"katex--inline\">A</span> ,  <span class=\"katex--inline\">B</span> ,  <span class=\"katex--inline\">C</span> ,  <span class=\"katex--inline\">D</span>  and  <span class=\"katex--inline\">E</span>  are replaced by the<br/>numbers 3, 5, 6, 7 and 9, although not necessarily in that order. The sums of the<br/>numbers at the ends of the line segments  <span class=\"katex--inline\">\\overline{AB}</span> ,  <span class=\"katex--inline\">\\overline{BC}</span> ,  <span class=\"katex--inline\">\\overline{CD}</span> ,  <span class=\"katex--inline\">\\overline{DE}</span> , and  <span class=\"katex--inline\">\\overline{EA}</span>  form an<br/>arithmetic sequence, although not necessarily in that order. What is the middle<br/>term of the arithmetic sequence?<br/><center><img class=\"latexcenter\" alt=\"[asy] draw((0,0)--(0.5,1.54)--(1,0)--(-0.31,0.95)--(1.31,0.95)--cycle); label(&#34;$A$&#34;,(0.5,1.54),N); label(&#34;$B$&#34;,(1,0),SE); label(&#34;$C$&#34;,(-0.31,0.95),W); label(&#34;$D$&#34;,(1.31,0.95),E); label(&#34;$E$&#34;,(0,0),SW); [/asy]\" height=\"235\" src=\"https://latex.artofproblemsolving.com/b/7/4/b742a9eaa62d04f46229732736080eeb97f05475.png\" width=\"252\"/></center></p>&#10;<p> <span class=\"katex--inline\">(\\mathrm {A}) \\ 9 \\qquad (\\mathrm {B}) \\ 10 \\qquad (\\mathrm {C})\\ 11 \\qquad (\\mathrm {D}) \\ 12 \\qquad (\\mathrm {E})\\ 13</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": 3, "problem_name": "2005 AMC 12A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc12A_p14", "prev": "/problem/05_amc12A_p12"}}