Let \(a\) be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle \(\alpha\) …

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 \((\sqrt{3}+1)x+(\sqrt{3}-1)y=0\) and \((\sqrt{3}-1)x-(\sqrt{3}+1)y+8\sqrt{3}=0\). Then \({a}^{2}\) is equal to

[JEE Main 2025, 8 Apr (Shift 1)]