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 :
(c): we use the property of \[{{\Delta }^{1e}}\] Sum of two sides > third side \[\Rightarrow AB+BC>AC\] \[BC+CD>BD\text{ }and\text{ }AB+AD>BD\] \[CD+AD>AC\] Adding these four inequations; \[2\left( AB+BC+CD+DA \right)>2\left( AC+BD \right)\] \[\Rightarrow AB+BC+CD+DA>AC+BD.\]
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