Question

Pleaseanswer fast
O is a point in the exterior of triangle ABC show that OA+OB+OC+>1/2(AB+BC+CA)
Answer fast please
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Answer 1

Step-by-step explanation:

We know that AB < AO + BO ( Sum of 2 sides of triangle is greater than 3)

similarly AC < AO + CO ( Sum of 2 sides of triangle is greater than 3)

BC < BO + CO ( Sum of 2 sides of triangle is greater than 3)

Now adding all LHS and RHS we get

⇒ AB + AC + BC < AO + BO + AO + CO + BO + CO

⇒ AB + AC + BC < 2AO + 2BO + 2CO

⇒ AB + AC + BC < 2(AO + BO + CO)

⇒ 1/2(AB + AC + BC) < AO + BO + CO

∴AO + BO + CO > 1/2(AB + AC + BC).

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