A triangle has corners points A, B, and C. Side AB has a length of #9 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #14 #, what is the length of side BC?

1 Answer
Jim G.
Jun 21, 2017

#BC=20 4/9#

Explanation:

#"let the point where the angle bisector intersects with side"#
#"BC be D"#

#"then using the "color(blue)"Angle bisector theorem"#

#color(red)(bar(ul(|color(white)(2/2)color(black)((AB)/(AC)=(BD)/(DC))color(white)(2/2)|)))#

#"require to find DC"#

#rArr9/14=8/(DC)#

#rArr9DC=14xx8larrcolor(blue)" cross-multiplying"#

#rArrDC=(14xx8)/9=112/9#

#rArrBC=BD+DC=8+112/9=184/9=20 4/9#

#BC=20 4/9larrcolor(red)" exact value"#

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