AMC 12 2010a Problem 17

Equiangular hexagon $ABCDEF$ has side lengths $AB=CD=EF=1$ and $BC=DE=FA=r$. The area of $\triangle ACE$ is $70\%$ of the area of the hexagon. What is the sum of all possible values of $r$?

\textbf{(A)}\ \frac{4\sqrt{3}}{3} \textbf{(B)} \frac{10}{3} \textbf{(C)}\ 4 \textbf{(D)}\ \frac{17}{4} \textbf{(E)}\ 6