A triangle has corners at points A, B, and C. Side AB has a length of $18$ $18$ . The distance between the intersection of point A's angle bisector with side BC and point B is $6$ $6$ . If side AC has a length of $14$ $14$ , what is the length of side BC?

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Answer 1 · 2016-04-30T07:50:39

$B C = 10.667$ $BC=10.667$

According to angle bisector theorem, in a $DeltaABC$ , if angle $A$ is bisected and it cuts $BC$ at $D$ , then

$(AB)/(AC)=(BD)/(DC)$

As $AB=18$ , $AC=14$ and distance between the intersection of point A's angle bisector with side BC and point B i.e. $BD$ is $6$ ,

we have $18/14=6/(DC)$

or $DC=(14xx6)/18=(14xx1cancel6)/(3cancel18)=14/3=4.667$

Hence $BC=6+4.667=10.667$

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A triangle has corners at points A, B, and C. Side AB has a length of 18 1818 . The distance between the intersection of point A's angle bisector with side BC and point B is 6 66 . If side AC has a length of 14 1414 , what is the length of side BC?