In triangle ABC, if L and M are the points on AB & AC respectively, such that LM is parallel to BC. If BM & CL intersect at O, prove that area of traingle LOB = area of triangle MOC.

 

 
Hi!
 
We have LM||BC
 
ΔBLC and ΔCMB are on same base BC and have the same height as LM||BC.
 
Therefore ar(ΔBLC) = ar (ΔCMB)
 
 ar(ΔLOB) + ar(ΔBOC) = ar(ΔMOC) + ar (ΔBOC)
 
  ar(ΔLOB) = ar(ΔMOC)
 
Cheers!

 

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Thank you sir..!

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