Problem
2005 AMC 10A Problem 17
In the five-sided star shown, the letters A, B, C, D, and E are replaced by the numbers 3, 5, 6, 7, and 9, although not necessarily in this order. The sums of the numbers at the ends of the line segments \overline{AB}, \overline{BC}, \overline{CD}, \overline{DE}, and \overline{EA} form an arithmetic sequence, although not necessarily in this order. What is the middle term of the arithmetic sequence?
![[asy] size(150); defaultpen(linewidth(0.8)); string[] strng = {'A','D','B','E','C'}; pair A=dir(90),B=dir(306),C=dir(162),D=dir(18),E=dir(234); draw(A--B--C--D--E--cycle); for(int i=0;i<=4;i=i+1) { path circ=circle(dir(90-72*i),0.125); unfill(circ); draw(circ); label("$"+strng[i]+"$",dir(90-72*i)); } [/asy]](/static/aops/e7ccece18535f75fcce290018f4a4aecbfa38461.png)
\textbf{(A) } 9\qquad \textbf{(B) } 10\qquad \textbf{(C) } 11\qquad \textbf{(D) } 12\qquad \textbf{(E) } 13
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