In a triangle ABC, AD is a median .Which is the correct answer ?
a) AB+AC > 2 AD
b) AB + AC < 2 AD
c) AB+AC = 2 AD
d) None of these
If you can use vectors then notice that $\displaystyle D$ is a midpoint so:
$\displaystyle \overrightarrow {AB} + \overrightarrow {BD} = \overrightarrow {AC} + \overrightarrow {CD} = \overrightarrow {AD} $
Using $\displaystyle \|\overrightarrow {BD}\|$ for the length of $\displaystyle \overrightarrow {BD}$ note also that $\displaystyle \|\overrightarrow {BD}\|=\|\overrightarrow {CD}\|$.
Ibdutt
Bravo..you did a good job...nice proof however you could use the Thales theorem as well
have a look here..
Intercept theorem - Wikipedia, the free encyclopedia.
However Plato is also right. If you consider vectors then the answer is c and not a.
In my opinion the original question is not clear. AB,AD AC are segments? or vectors?