Question

2. O is any point inside the triangle A ABC. Let's prove that (i) AB+AC > OB+OC (ii) AB+BC+AC > OA+OB+OC ​

Answer 1

Answer:

This is the correct once....

Step-by-step explanation:

InΔPBO

BP+PO>OB

AddingOCanbothsides

weget,

BP+PO+OC>OB+OC

BP+PC>OB+OC

BP+PC>OB+OC→(i)[PO+OC=PC]

InΔAPC

AP+AC>PC

AddingBPonbothsides,weget

AP+AC+BP>PC+BP→(ii)[AP+PB=AB]

from(i)&(ii)

AB+AC>BP+PC>OB+OC

AB+AC>OB+OC→(iii)

similarly

BC+AC>OB+OA→(iv)

AB+BC>OA+OC→(v)

addingequation(3)(4)(5)weget

2(AB+BC+CA)>2(OA+OB+OC)

AB+BC+CA>OA+OB+OC