Question bank/JEE Main/Mathematics

Consider a $\Delta$ABC and let a, b and c denote the lengths of
the sides opposite to vertices A, B and C respectively AD be a median of
the $\Delta$ABC. If AE and AF are medians of the triangle ABD and ADC
respectively and AD = m_1, AE = m_2, AF = m_3 then $\frac{a^{2}}{8}$
is equals to.

A$m_{2}^{2} + m_{3}^{2} - 2m_{1}^{2}$B$m_{1}^{2} + m_{2}^{2} - 2m_{3}^{2}$C$m_{1}^{2} + m_{3}^{2} - 2m_{2}^{2}$D$m_{1}^{2} + m_{2}^{2} - m_{3}^{2}$

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Source: Grass-G / M-24 Mathematics Paper 31 Dec.docx