Question

7. If O is
a point in the exterior of ABC, show that
2(OA +OB + OC) > (AB + BC + CA).
Hint. Join OA, OB, OC
From Triangle AOB, OA+OB> AB.
From Triangle BOC, OB+OC>BC
From Triangle AOC, OA+OC>CA.

Refer to the attached picture for information


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Answer 1

Answer:

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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