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Question

The median AD of the ΔABC is bisected at E, BE meets AC in F, then AF: AC is equal to

A
34
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B
13
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C
12
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D
14
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Solution

The correct option is B 13
Taking A as the origin let the position vectors of B and C be b and c respectively. Equations of lines BF and AC are r=b+λ(b+c4b) and r=0+μc respectively. For the point of intersection F. We have
b+λ(c3b4)=μc
13λ4=0 and λ4=μ
λ=43 and μ=13
Therefore, the position vector of F is r=13c
Now, AF=c3AF=13AC
Hence, AF:AC=13:1=13

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