Question
Wed February 09, 2011 By: Sanya Wason
 

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.

Expert Reply
Fri February 11, 2011
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.
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