3. In $\triangle A B C$, it is known that $B C=10, A C>A B$, and the medians $B E, C F$ are perpendicular to each other, and the distance from the centroid $G$ to $B C$ is 3. Try to find the lengths of $A B, A C$. (1987, Shanghai Junior High School Competition)
(Solution: $A B=\sqrt{130}, A C=\sqrt{370}$ )