Prove that in a quadrilateral the sum of all sides is greater than the sum of its diagonals .
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Answer: AB+BC+CD+DA>AC+BD
In∠ABC
AB+BC>AC−(1)
In∠ACD
AD+CD>AC−(2)
In∠ABD
AB+AD>BD−(3)
In∠BCD
BC+CD>BD−(4)
2(AB+BC+CD+DA)>2(AC+BD)
AB+BC+CD+DA>AC+BD
Hence proved
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