Question

if ABCD is a quadrilateral whose diagonals AC and BD intersect at O, prove that (1)(AB+BC+CD+DA)>(AC+BD)

Answer 1

let the quadrilateral is ABCD
now we will use the property of a triangle
thay sum of any two sides of a triangle is always greater than third side

in ∆ABC
AB + BC > AC

Similarly In ∆BCD
BC + CD > BD

In ∆ CDA
CD + DA > AC

In ∆DAB
DA + AB > BD

adding all the equations we get
2(AB+BC+CD+DA) > 2(AC+BD)

So
(AB+BC+CD+DA) > (AC+BD)

Answer 2

Hope it helps you

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