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AD is the median of triangle ABC and M is the mid point of AD. also BM produced meets AC at N . Prove that AN=1/3 AC.

Asked by sanya wason 9th February 2011, 4:10 PM
Answered by Expert
Answer:
Dear Student,
Here is the solution:
Through D, Draw DK||BN.
In triangleADK, M is the mid-point of AD and MN||DK.
Therefore, N is the mid-point of AK.
Hence, AN=NK.............(i)
In triangleBCN, D is the mid-point of BC and BN||DK.
Therefore, K is the mid-point of NC.
Hence, KC=NK.............(ii)
From (i) and (ii),
AN=NK=KC..............(iii)
Now, AC=AN+NK+KC
AC=AN+AN+AN
AC=3AN
therefore, AN=1/3AC.
Hence proved.
Regards
Team Topperlearning.
Answered by Expert 11th February 2011, 10:18 AM
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