Question

AD is a median of the triangle ABC. Is it true that AB+BC+CA > 2 AD?
If True enter 1 else if False enter 0.

Answer 1

Given, $△ABC$, $AD$ is median of triangle, on side $BC$
Now, In $△ABD$,
$AB+BD>AD$ (Sum of two sides of triangle is greater than the third side)
Now, In $△ACD$,
$AC+CD>AD$ (Sum of two sides of triangle is greater than the third side)
Thus, adding both,
$AB+BD+AC+CD>2AD$
$AB+AC+BC>2AD$