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E is the mid-point of a median AD of ΔABC and BE is produced to meet AC at F. Show that AF = 1/3 AC.

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Given, a ABC in which AD is a median and E is mid-point of AD. Now, drawing DP||EF.

In ΔADP, E is mid-point of AD and EF||DP.

imageF is mid-point of AP.

In ΔFBC, D is mid-point of BC and DP||BF.

imageP is mid-point of FC.

Thus, AF = FP = PC

Hence, AF = 1/3 AC

Hence, proved.

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