In Fig. 6.22, line segment \( \mathrm{DF} \) intersect the side \( \mathrm{AC} \) of a triangle ...

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In Fig. 6.22, line segment \( \mathrm{DF} \) intersect the side \( \mathrm{AC} \) of a triangle \( \mathrm{ABC} \) at the point \( E \) such that \( E \) is the mid-point of \( C A \) and \( \angle A E F=\angle A F E \). Prove that \( \frac{\mathrm{BD}}{\mathrm{CD}}=\frac{\mathrm{BF}}{\mathrm{CE}} \)
[Hint: Take point \( \mathrm{G} \) on \( \mathrm{AB} \) such that \( \mathrm{CG} \| \mathrm{DF} \) ]
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