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In a quadrilateral ABCD, show that (AB+...

In a quadrilateral ABCD, show that `(AB+BC+CD+DA)lt2(BD+AC).`

Text Solution

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`OA+OB gt AB, OB +OC gt BC,`
`OC+ODgtCD,OD+OAgtDA.`
Adding, we get
`2(OA+OC+OB+OD)gt(AB+BC+CD+DA)`
`rArr" "2(AC+BD)gt(AB+BC+CD+DA)`
`" "[because OA+OC=AC,OB+OD=BD].`
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