The area of trapezoid $ABCD$ is $164\ \text{cm}^2$. The altitude is $8\ \text{cm}$, $AB$ is $10\ \text{cm}$, and $CD$ is $17\ \text{cm}$. What is the length of $BC$, in centimeters?

Let's think step by step and output the final answer within \boxed{}.
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