Determine the centroidal polar moment of inertia $J_{C}$ of the 25 -in $^{2}$ shaded area knowing that the polar moments of inertia of the area with respect to points $A, B,$ and $D$ are, respectively, $J_{A}=281 \mathrm{in}^{4}$, $J_{B}=810 \mathrm{in}^{4},$ and $J_{D}=1578 \mathrm{in}^{4}$.