In triangle $ABC,$ the length of side $\overline{BC}$ is equal to the average of the other two sides.  Also,
\[\cos C = \frac{AB}{AC}.\]Given that all the side lengths are integers, find the smallest possible area of triangle $ABC.$
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In triangle $ABC,$ the length of side $\overline{BC}$ is equal to the average of the other two sides.  Also,
\[\cos C = \frac{AB}{AC}.\]Given that all the side lengths are integers, find the smallest possible area of triangle $ABC.$
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6 \sqrt{6}
In triangle $ABC,$ the length of side $\overline{BC}$ is equal to the average of the other two sides.  Also,
\[\cos C = \frac{AB}{AC}.\]Given that all the side lengths are integers, find the smallest possible area of triangle $ABC.$
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