Coordinate Geometry: JEE Main 2024 Mathematics question

A square is inscribed in the circle $x^2+y^2-10 x-6 y+30=0$. One side of this square is parallel to $y=x+3$. If $\left(x_i, y_i\right)$ are the vertices of the square, then $\Sigma\left(x_i^2+y_i^2\right)$ is equal to: