Question

M is a point on side BC of a triangle ABC such that AM is the bisector of $\angle BAC.$ Is it true to say that perimeter of the triangle is greater than 2 AM? If True enter 1, else if False enter 0.

Answer 1

Given, $△ABC$, $AM$ is bisector of $\angle BAC$
Now, In $△ABM$,
$AB+BM>AM$ (Sum of two sides of triangle is greater than the third side)
Now, In $△ACM$,
$AC+CM>AM$ (Sum of two sides of triangle is greater than the third side)
Thus, adding both,
$AB+BM+AC+CM>2AM$
$AB+AC+BC>2AM$