MOM from summed squared distances

Suppose $X_1,…,X_{10},Y_1,…,Y_{10}$ are independent random variables, where $X_i\sim N(0,\sigma^2)$ and $Y_i\sim N(0,3\sigma^2)$ for $i=1,2,…,10$. The observables are $D_1,…,D_{10}$, where $D_i$ denotes the Euclidean distance between the points $(X_i,Y_i,0)$ and $(0,0,5)$ for $i=1,2,…,10$. If the observed value of $\sum_{i=1}^{10}D_i^2$ is equal to $1050$, then the method of moments estimate of $\sigma^2$ is equal to __________ (answer in integer)