Question

In triangle $ABC,D$ is any point on side $BC$, then:

$AB+BC+AC>2AD$

• A. True
• B. False

Answer 1

The correct option is A True

In triangle ABD,
$AB+BD>AD$ [because, the sum of any two sides of a triangle is always greater than the third side]
In triangle $ADC$,
$AC+DC>AD$ [because, the sum of any two sides of a triangle is always greater than the third side]
Adding these we get,
$AB+BD+AC+DC>AD+AD$
$\Rightarrow AB+(BD+DC)+AC>2AD$
$\Rightarrow AB+BC+AC>2AD$
Hence proved