# Median question

• Jun 15th 2013, 10:20 AM
sscgeek
Median question
In a triangle ABC, AD is a median .Which is the correct answer ?

b) AB + AC < 2 AD

d) None of these
• Jun 15th 2013, 10:41 AM
Plato
Re: Median question
Quote:

Originally Posted by sscgeek
In a triangle ABC, AD is a median .Which is the correct answer ?
b) 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}\|\$.
• Jun 16th 2013, 02:24 AM
ibdutt
Re: Median question
• Jun 16th 2013, 03:39 AM
MINOANMAN
Re: Median question
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?