In a trapezium \( \mathrm{ABCD}, \mathrm{AB} \| \mathrm{DC} \) and \( \mathrm{DC}=2 \mathrm{AB} ...

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In a trapezium \( \mathrm{ABCD}, \mathrm{AB} \| \mathrm{DC} \) and \( \mathrm{DC}=2 \mathrm{AB} . \mathrm{EF} \) drawn parallel to \( A B \) cuts \( A D \) in \( F \) and \( B C \) in \( E \) such that \( \frac{\mathrm{BE}}{\mathrm{EC}}=\frac{3}{4} \). Diagonal \( \mathrm{DB} \) intersects \( \mathrm{EF} \) at \( \mathrm{G} \). Prove that \( 7 \mathrm{FE}=10 \mathrm{AB} \).
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