The image displays two geometric diagrams. The first is an isosceles triangle ABC with AD as the altitude. AB = AC = 8 and AD = 9. The second diagram shows a triangle with a vertex labeled A and a side labeled 18.

Since $\triangle ABC$ is an isosceles triangle with $AB = AC$, the altitude $AD$ to the base $BC$ also bisects the base. This means $BD = DC$. Also, $AD$ is perpendicular to $BC$, forming two right-angled triangles, $\triangle ADB$ and $\triangle ADC$.

In the right-angled triangle $\triangle ADC$, we have the hypotenuse $AC = 8$ and one leg $AD = 4$. We can find the length of the other leg $DC$ using the Pythagorean theorem: $AD^2 + DC^2 = AC^2$.

Take the square root of both sides to find $DC$:

To simplify the radical, find the largest perfect square factor of 48, which is 16:

Since $AD$ bisects $BC$, $BC = 2 \times DC$.

The length of $BC$ is $\boxed{\mathbf{8\sqrt{3}}}$.