Question

In a ABC, AD is a median & E is the midpoint of AD. If BE is produced, it meets AC in F. Show that AF=1/3AC.

Answer 1

.Given AD is the median of ΔABC and E is the midpoint of ADThrough D, draw DG || BF In ΔADG, E is the midpoint of AD and EF || DG By converse of midpoint theorem we have F is midpoint of AG and AF = FG   → (1) Similarly, in ΔBCF  D is the midpoint of BC and DG || BF    G is midpoint of CF and FG = GC → (2) From equations (1) and (2), we get AF = FG = GC → (3)From the figure we have, AF + FG + GC = AC AF + AF + AF = AC [from (3)] 3





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