In Fig. , line segment \( \mathrm{DF} \) intersect the side \( \mathrm{AC} \) of a triangle \( \...

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In Fig. , line segment \( \mathrm{DF} \) intersect the side \( \mathrm{AC} \) of a triangle \( \mathrm{ABC} \) at the point \( \mathrm{E} \) such that \( \mathrm{E} \) is the mid-point of \( \mathrm{CA} \) and \( \angle \mathrm{AEF}=\angle \mathrm{AFE} \). Prove that
QV
\[
\frac{\mathrm{BD}}{\mathrm{CD}}=\frac{\mathrm{BF}}{\mathrm{CE}} \text {. }
\]
[Hint: Take point \( \mathrm{G} \) on \( \mathrm{AB} \) such that CG \( \| \) DF.]
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