Question

AD is a median of the triangle ABC.O is the midpoint of AD.extended BO intersects AC at the point E.Prove that BO=3OE.​

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AD is a median of triangle ABC and E is the midpoint of AD. BE produced meets AC in F, Prove that AF 1/3 AC

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ANSWER

given:-

AD is the median of ΔABC and E is the midpoint of AD

Through 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 will get

AF=FG=GC........3

AF+FG+GC=AC

AF+AF+AF=AC ......... from eq 3

AF=AC

AF=(1/3)AC

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