Question

ABCD is a quadrilateral.Is
AB+BC+CD+DA<2(AC+BD)?

Answer 1

Answer:

ABCD is a quadrilateral

to prove = AB+BC+CD+DA<2(AC+BD)

Proof

in triangle DOC

DO+OC=CD - 1

in triangle COBAP+

CO+OB=BC - 2

In triangle BOA

BO+OA=AB - 3

In triangle AOD

AO+OD=DA - 4

Add 1,2,3 & 4, we get

DO+OC+CO+OB+BO+OA+AO+OD= CD+BC+AB+DA

2(DO+CO+BO+AO)=CD+BC+AB+DA-(AO+BO=AB,BO+OC=BC,CO+DO=CD,DO+AO=DA)

2(AB+BC+CD+DA)=AC+BD-(AB+CD=BD,BC+DA=AC)

AB+BC+CD+DA<2(AC+BD)

HENCE PROVED