A triangle has corners points A, B, and C. Side AB has a length of $12$ $12$ . The distance between the intersection of point A's angle bisector with side BC and point B is $4$ $4$ . If side AC has a length of $10$ $10$ , what is the length of side BC?

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Answer 1 · 2016-04-29T09:19:44

$B C = 7.333$ $BC=7.333$

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 $AB=12$ , $AC=10$ and distance between the intersection of point A's angle bisector with side BC and point B i.e. $BD$ is $4$ ,

we have $12/10=4/(DC)$

or $DC=(10xx4)/12=(10xxcancel4)/(3cancel12)=10/3=3.333$

Hence $BC=4+3.333=7.333$

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A triangle has corners points A, B, and C. Side AB has a length of 12 1212 . The distance between the intersection of point A's angle bisector with side BC and point B is 4 44 . If side AC has a length of 10 1010 , what is the length of side BC?