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Math Help - Problem involving Similarities!

  1. #1
    Junior Member Kaloda's Avatar
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    Problem involving Similarities!

    Given triangle ABC with AB > AC. The bisectors of the interior and exterior angles at A intersect line BC at points D and E, respectively.

    PROVE that:
    ((sqrt (AD^2+AE^2)) / CD) - (sqrt (AD^2+AE^2)) / BD = 2
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  2. #2
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    Hello, Kaloda!

    I haven't solve this yet, but I have some observations.


    \text{Given }\Delta ABC\text{ with }AB > AC.

    \text{The bisectors of the interior and exterior angles at }A
    . . . \text{intersect line }BC\text{ at points }D\text{ and }E\text{, respectively.}

    \text{Prove that: }\:\dfrac{\sqrt{AD^2+AE^2}}{CD} - \dfrac{\sqrt{AD^2+AE^2}}{BD} \:=\: 2

    The bisectors of an interior angle and its exterior angle are perpendicular.

    . . Hence: . \angle DAE = 90^o\:\text{ and }\: \sqrt{AD^2 + AE^2} \:=\:DE

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  3. #3
    Junior Member Kaloda's Avatar
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    Last edited by Kaloda; November 26th 2010 at 04:48 AM.
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  4. #4
    Junior Member Kaloda's Avatar
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    tnx ... that's what i need ...
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