Question

O is any point in the interior of $\Delta ABC.$ then
$AB+AC<OB+OC$ is true /false

• A. True
• B. False

Answer 1

The correct option is B False

Here, $O$ is any point in the interior of $△ABC.$

$E,F$ points on sides $AB$ and $AC.$

We know that, the sum of any two sides of triangle is always greater than third.

In $△ABF$

$AB+AF>BF$

$AB+AF>OB+OF$ ------ ( 1 )

In $△COF$

$CF+OF>OC$ ------ ( 2 )

Adding equations ( 1 ) and ( 2 ) we get,

$\Rightarrow$ $AB+AF+CF+OF>OB+OF+OC$

$\Rightarrow$ $AB+AF+CF>OB+OC$

$\Rightarrow$ $AB+AC>OB+OC$

$\therefore$ We can see given statement in question id false.