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

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- Jun 15th 2013, 10:20 AMsscgeekMedian question
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 - Jun 15th 2013, 10:41 AMPlatoRe: Median question
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 AMibduttRe: Median question
- Jun 16th 2013, 03:39 AMMINOANMANRe: 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?