JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

In a tetrahedron $O A B C$, the edges are of lengths, $|O A|=|B C|=a,|O B|=|A C|=b,|O C|=|A B|=c$. Let $G_1$ and $G_2$ be the centroids of the triangle $A B C$ and $A O C$ such that $O G_1 \perp B G_2$, then the value of $\frac{a^2+c^2}{b^2}$ is