ABCD is a quadrilateral in which diagonal AC and BD intersect at O. show that AB+BC+CD+DA > AC + BD
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Sol: In ABC , By inequality property of triangle,
AB + BC > AC -------(1)
In BCD , By inequality property of triangle,
BC + CD > BD -------(2)
In ADC , By inequality property of triangle,
CD + DA > AC -------(3)
In ABD , By inequality property of triangle,
DA + AB > BD -------(4)Add equation (1)(2)(3) and (4)
AB+BC+BC+CD+CD+DA+DA+AB > AC+BD+AC+BD
2(AB+BC+CD+DA)>2(AC+BD)
AB+BC+CD+DA > AC+BD
Hence Proved
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