Angle Bisector Question

Feb 2008
51
0
Istanbul
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
 

Attachments

Dec 2007
3,184
558
Ottawa, Canada
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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Reactions: carlsmith
Feb 2008
51
0
Istanbul
Yes the question asks the length of |BC|=x and I agree with alt the statements you have written.
 
Dec 2007
3,184
558
Ottawa, Canada
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 (Nerd)
 
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Reactions: JohnDoe
Feb 2008
51
0
Istanbul
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.