A) \[\left( AB+BC+CD+DA \right)<\left( AC+BD \right)\]
B) \[\left( AB+BC+CD+DA \right)>2\left( AC+BD \right)\]
C) \[\left( AB+BC+CD+DA \right)>\left( AC+BD \right)\]
D) \[AB+BC+CD+DA=2\,\left( AC+BD \right)\]
Correct Answer: C
Solution :
In \[\Delta \,\,ABC,\,\,\Delta \,\,ACD,\,\,\Delta \,\,BCD\]and \[\Delta \,\,ABD\] AB + BC > AC CD + DA > AC BC + CD >BD DA + AB > BD Adding above inequalities 2 (AB + BC + CD +DA) > 2 (AC+ BD) \[\Rightarrow \](AB + BC +CD DA) > (AC + BD)You need to login to perform this action.
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