6. Given that $O$, $G$, and $H$ are the circumcenter, centroid, and orthocenter of $\triangle ABC$ respectively, $BC=a$, $CA=b$, $AB=c$, and the radius of the circumcircle of $\triangle ABC$ is $R$. Then among the following conclusions:
(1) $O G^{2}=R^{2}-\frac{1}{9}\left(a^{2}+b^{2}+c^{2}\right)$,
(2) $O G^{2}=\frac{1}{9}\left(a^{2}+b^{2}+c^{2}\right)-R^{2}$,
(3) $O H^{2}=9 R^{2}-\left(a^{2}+b^{2}+c^{2}\right)$,
(4) $O H^{2}=9\left(a^{2}+b^{2}+c^{2}\right)-R^{2}$, the correct ones are ( ).
(A)(1)(3)
(B) (2) (4)
(C)(1)(4)
(D)(2)(3)
6. A