Mathematics Question from JEE Main 2025 · 8 April, Shift 2

Let $a$ be the length of a side of a square $OABC$ with $O$ being the origin. Its side $OA$ makes an acute angle $\alpha$ with the positive $x$-axis and the equations of its diagonals are $\left( \sqrt{3} + 1 \right) x + \left( \sqrt{3} - 1 \right) y = 0$ and $\left( \sqrt{3} - 1 \right) x - \left( \sqrt{3} + 1 \right) y + 8\sqrt{3} = 0.$ Then $a^2$ is equal to