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Question

In a ABC,E and F are the mid-point AB and AC respectively. Point M and N on sides AB and AC respectively such that AM=14AB and AN =14 AC. Prove that MN=14BC

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Solution

Now, from ABC we have, E & F one mid-points of AB & AC respectively.
Then we have, EFBC & EF=1/2BC(1)
Again from AEF we have,
M & N are mid points of AE & AF Then we get, MNEF & MN=1/2EF(2)
Using (1) in (2) we get, MN=1/2×12×BC
=(14BC)

1355451_1198867_ans_c5a6a64902864d9b947bc504f63eb1c1.png

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