O is a point in the interior of triangle ABC. Use the symbols( =) to make the following statements true.
A. OA+OB. ... .......AB
b. OA+OC ............AC
c.OB +OC. ............BC
now,show that AB+AC+AB

Answer :

We form our diagram from given information , As :

We know from the triangle inequality theorem that any side of a triangle is always shorter than the sum of the other two sides.

So,

A )  OA  +  OB  >  AB                                                                 ( Ans )

B )  OA  +  OC  >  AC                                                                 ( Ans )

B )  OB  +  OC  >  BC                                                                 ( Ans )

Now we add all thee equation and get

OA  +  OB + OA  +  OC  + OB  +  OC >  AB + AC + BC

2 ( OA + OB + OC ) > AB  + AC  + BC                                                                 ( Ans )