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In taingle ABC,DE parallel too AC …

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In taingle ABC,DE parallel too AC and DC parallel AP. Prove thatBE/EC=BC/CP
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In △BPA, we have

   DC∣∣AP       [Given]

Therefore, by basic proportionality theorem, we have

BC/ CP ​= BD​/DA ........ (I)

In △BCA, we have

 DE∣∣AC

Therefore, by basic proportionality theorem, we have

BE/EC ​ = BD​/DA........ (iI)

From (i) and (ii), we get

 BC/CP ​= BE/ EC ​ or BE/​EC = BC/CP​        [Hence proved]

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