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Question
In a triangle ABC, AD is a median and E is mid-point of median AD. A line through B and E meets AC at point F.
Prove that: AC = 3AF.
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Solution
The required figure is shown below
For help, we draw a line DG || BF
Now from triangle ADG, DG || BF and E is the midpoint of AD
Therefore, F is the midpoint of AG, i.e; AF = FG ...(1)
From triangle BCF, DG || BF and D is the midpoint of BC
Therefore, G is the midpoint of CF, i.e; FG = GC …(2)
AC = AF + FG + GC
= AF + AF + AF
AC = 3AF ...(From (1) and (2))
Hence, proved.
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