\( A D \) is median of the \( \triangle A B C \). If \( A E \) and \( A F \) are medians of the ...

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\( A D \) is median of the \( \triangle A B C \). If \( A E \) and \( A F \) are medians of the triangles \( A B D \) and \( A D C \) respectively, and \( A D=m_{1}, A E=m_{2}, A F=m_{3} \), then \( \frac{a^{2}}{8} \) is
(a) \( m_{2}^{2}+m_{3}^{2}-2 m_{1}^{2} \)
(b) \( m_{1}^{2}+m_{2}^{2}-2 m_{3}^{2} \)
(c) \( \mathrm{m}_{2}^{2}+\mathrm{m}_{3}^{2}-\mathrm{m}_{1}^{2} \)
(d) none of these
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