Let \( \vec{a} \) and \( \vec{b} \) be the vectors of the same magnitude such that \( \dfrac{|\vec{a}+\vec{b}| + |\vec{a}-\vec{b}|}{|\vec{a}+\vec{b}| - |\vec{a}-\vec{b}|} = \sqrt{2} + 1 \). Then \( \dfrac{|\vec{a}+\vec{b}|^{2}}{|\vec{a}|^{2}} \) is:
\( 4 + 2\sqrt{2} \)
\( 1 + \sqrt{2} \)
\( 2 + 4\sqrt{2} \)
\( 2 + \sqrt{2} \)
