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

Construct the figure correctly....U will see, AL=LB=y(say)...and CN=x,AN=2x(according to the question)...Now in case of triangle AML and ANB ,ML is parallel to NB...make the base angles equal by corresponding angle property of parallel lines hence prove the triangles similar...therefore BY Basic proportionality theorem...AL/LB=AM/MN..(AL/LB=1)...AM=MN...AM+MN=2x....AM=MN=x....therefore. AM=MN=CN=x. Hence proved