Question 27
In the diagram, $ABC$ is a triangle such that $AB$ is longer than $AC$. The point $N$ lies on $BC$ such that $AN$ bisects $\angle BAC$. The point $G$ is the centroid of $\triangle ABC$, and $GN$ is perpendicular to $BC$. Suppose $AC=6\text{ cm}$, $BC=5\sqrt3\text{ cm}$ and $AB=x\text{ cm}$. Find $x$.
