Question

o is a point in the exterior of triangle ABC.
Show that
OA + OB +OC is greater than 1/2 (AB+ Be + CA)​

Answer 1

Step-by-step explanation:

Taking ∆OBC

1) OB+OC>BC ………Sum of the two sides of a triangle is greater than the third side

In ∆OAC

2) OA+ OC> AC ……reason same as above.

In ∆OAB

3 ) OA +OB >AB ……..reason same as above

Adding 1) 2) & 3)

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

2OA+2OB + 2OC >AB+ BC+ AC

Dividing both sides by 2

(OA + OB +OC)>1÷2(AB +BC+AC ) proved.