Question

O is a point that lies in the interior of $\Delta ABC$. Then $2(OA-OB-OC)>\text{Perimeter}of\Delta ABC$.

• A. True
• B. False

Answer 1

The correct option is B False

From the $△ABC,$ by triangle inequality,

$OA+OB>AB$ ....... $\left(i\right)$

$OB+OC>BC$ ........ $\left(ii\right)$

$OA+OC>AC$ ........ $\left(iii\right)$

By adding $\left(i\right),\left(ii\right)$ and $\left(iii\right)$

$2(OA+OB+OC)>AB+BC+AC$

$\therefore 2(OA+OB+OC)>\text{Perimeter of triangle}ABC$

Hence, the statement is false.