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Math Help - Angle Bisector Question

  1. #1
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    Post Angle Bisector Question

    Hello everyone I have a question which I can not find the answer or the method. Please have a look at the attachment(x=? answer is 6) and I would be grateful if you show intermediate steps. Thanks
    Attached Thumbnails Attached Thumbnails Angle Bisector Question-tarama0003.jpg  
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  2. #2
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    Your diagram seems to mean the following:

    triangle ABC, with side AB = 12

    D on BC such that AD bisects angleBAC

    E on AC such that ED bisects angleBEC and AF = DF, F being crossing point of AD and BE

    Question being: what is length of BF?

    AGREE??
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  3. #3
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    Yes the question asks the length of |BC|=x and I agree with alt the statements you have written.
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  4. #4
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    OK. I'll get you started:

    Let angleBAC = 2u and angleBEC = 2v ; then:

    angleAFE = 2v - u

    angleADE = v - u ; so v > u

    angleABE = 2(v - u) ; so twice angleADE

    That's the limit of my help; hope someone else steps in
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  5. #5
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    The two angle bisectors intersect at a point(D) where the other exterior angle bisector should pass. So BD is an angle bisector two and we can write exterior angle bisector formula and find x=6. Hope I have explained it well. Thanks for your help BTW.
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