\( \mathrm{XY} \) is a line parallel to side \( \mathrm{BC} \) of a triangle \( \mathrm{ABC} \)....

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\( \mathrm{XY} \) is a line parallel to side \( \mathrm{BC} \) of a triangle \( \mathrm{ABC} \). If \( \mathrm{BE} \| \mathrm{AC} \) and \( \mathrm{CF} \| \mathrm{AB} \) meet \( \mathrm{XY} \) at \( \mathrm{E} \) and \( \mathrm{F} \) respectively, show that
\[
\operatorname{ar}(\mathrm{ABE})=\operatorname{ar}(\mathrm{ACF})
\]
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