Question

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 : AM=CN.
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Answer 1

In ΔABN , L is a midpoint and LM is parallel to BN
⇒M is the mid-point of AN(by MPT)
given,
AN=2CN
⇒2AM=2CN( M is midpoint , so AM=MN)
⇒AM=CN