Question

If O is a triangle within triangle ABC, SHOW that (¡) AB+AC>OB+OC (¡¡) AB+BC+CA>OA+OB+OC. (¡¡¡) OA+OB+OC>1/2(AB+BC+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.

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