Question : In a $\triangle ABC$, the median AD, BE, and CF meet at G, then which of the following is true?
Option 1: 4(AD + BE + CF) > 3(AB + BC + AC)
Option 2: 2(AD + BE + CF) > (AB + BC + AC)
Option 3: 3(AD + BE + CF) > 4(AB + BC + AC)
Option 4: AB + BC + AC > AD + BE + CF
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Correct Answer: AB + BC + AC > AD + BE + CF
Solution :
AB + AC > 2AD -------------(i)
AB + BC > 2BE -------------(ii)
AC + BC > 2CF -------------(iii)
Adding (i), (ii), and (iii)
⇒ 2(AB + BC + AC) > 2 (AD + BE + CF)
⇒ AB + BC + AC > AD + BE + CF
Hence, the correct answer is AB + BC + AC > AD + BE + CF.
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