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Thread: Median question

  1. #1
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    Median 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
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  2. #2
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    Re: Median question

    Quote Originally Posted by sscgeek View Post
    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 $\displaystyle \|\overrightarrow {BD}\|=\|\overrightarrow {CD}\|$.
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  3. #3
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    Re: Median question

    Median question-16-jun-13-2.png
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  4. #4
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    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?
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