A triangle has corners at points A, B, and C. Side AB has a length of #6 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #9 #, what is the length of side BC?

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Answer 1 · 2017-12-21T09:56:49

Length of side BC = 10

Let the point where the angle bisector intersects with
side BC be D

#"using the "color(blue)"angle bisector theorem"#

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

#6 / 9 = 4 / (DC)#

#DC = (4*9) / 6 = 6#

#BC = BD+DC= 4+6 =10#