In the adjoining figure, and are the medians of and Show that

Here in AD and BE are medians.


Hence, in ABC, we have:
AC = AE + EC


But AE = EC … as E is midpoint of AC


AC = 2EC …(1)


Now in ∆BEC,


DF || BE


Also, EF = CF … by midpoint theorem, as D is the midpoint of BC


But,


EC = EF + CF


EC = 2 CF …(2)


From 1 and 2, we get,


AC = 4 CF



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