Question

If O is any point in the interior angle of AABC, show that AB + BC + CA< 2(OA + OB + OC).​

Answer 1

In triangle ABC, O is a point interior of ∆ABC

As we know that “The sum of any  two sides of a triangle is greater than the third side”. OA + OB > AB …(i)

OA + OC > AC …(ii) and

OB + OC > BC …(iii)

Now, adding (i), (ii) and (iii), we get

2(OA + OB + OC) > AB + BC + CA

or AB + BC + CA < 2(OA + OB + OC)

Hence proved.