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Thread: Triangle Angle bisector problem

  1. #1
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    Triangle Angle bisector problem

    If you have a triangle ABC where AB=8, BC=4, and D is a point on AC where BD is a straight line that bisects angle B, and angle B is 120 degrees, what is the length of BD?

    I tried using cosine law where AC=sqrt(88), angle C = arcsin(8sin(120 degrees)/sqrt(88)), angle BDC = 120-angle C and BD was thus (4*angle C)/(120-angle BDC), but I think I messed up somewhere?
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  2. #2
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    Re: Triangle Angle bisector problem

    https://en.wikipedia.org/wiki/Angle_bisector_theorem
    With your triangle:
    AB / AD = BC / DC

    That'll lead you to AD = 2*CD
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  3. #3
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    Re: Triangle Angle bisector problem

    Extend side AB to the point E where BE=BC

    ABD and AEC are similar

    $\frac{\text{AB}}{\text{AE}}=\frac{\text{BD}}{ \text {EC}}$
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