14. If O is a point within AABC, show that
(i) AB + AC > OB + OC
(ii) AB + BC + CA >OA +OB + OC
(ii) OA + OB+ OC > Ž (AB + BC + CA).
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ronda
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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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