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ABC is a triangle in which L is the midpoint of AB and N is a point on AC such that AN=2CN. A line through L.parallel to BN meets AC at M.Prove that :

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In ΔABN , L is a midpoint and LM is parallel to BN
⇒M is the mid-point of AN(by MPT)
⇒2AM=2CN( M is midpoint , so AM=MN)
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given that , 
   L is the midpoint of side AB of ΔABC and N is the point on AC i.e. AN = 2CN .
We have to prove - AM = CN 
 Proof , 
  in Δ ANB .
  By using convs. of  midpoint theoram  .
   M is also a midpoint of AN 
 ⇒ AM = MN 
   now , 
 AN = 2CN 
also ,  AM + MN = 2CN 
        AM + AM ( because AM = MN ) = 2 CN 
        2AM = 2  CN 
     .'. AM = CN ( Proved ).................
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