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# Quick Question

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Points $F$, $E$, and $D$ are on the sides $\overline{AB}$, $\overline{AC}$, and $\overline{BC}$, respectively, of right $\triangle ABC$ such that $AFDE$ is a square. If $AB = 12$ and $AC = 8$, then what is $AF$?

I heard latex works on this site so I'm going to try it out.

Thanks!

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ElectricPavlov  Feb 8, 2018
edited by Guest  Feb 8, 2018
edited by Guest  Feb 8, 2018
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This bisects  angle   BAC

And an apex angle that is bisected sets up the following relationship :

AB / AC  =   DB / DC

12/8  = DB /DC   (1)

But   DF  is parallel to base  CA....so  it splits sides  AB and AC proportionally

Thus

DB /DC  =  FB / FA

Subbing  (1)....we have that

12/8  = FB / FA

Thus.....side BA  is split into 20 equal parts......and  FA  =  AF  is 8 of these

So.... AF  =

(8/20) (12)  =  96/20  =   4.8

CPhill  Feb 8, 2018
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