A triangle has corners at points A, B, and C. Side AB has a length of #24 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #35 #, what is the length of side BC?

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Answer 1 · 2017-12-21T08:56:11

Length of BC = 22.125

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

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

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

#24 / 35 = 9 / (DC#

#DC = (9*35) / (24) = 13.125#

#BC = BD+DC= 9+13.125 =22.125#