A triangle has corners points A, B, and C. Side AB has a length of #12 #. 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 #18 #, what is the length of side BC?

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Answer 1 · 2016-06-17T17:21:52

#BC=10.#

Let the angle-bisector of #/_A# meet BC in pt. #D.#

then, by the property of angle-bisector, we have #(BD)/(DC)=(AB)/(AC)............(1)#

But, given that, #BD=4,AB=12, AC=18.#

#:.# by #(1),# 4/(DC)=12/18=4/6.#

Evidently, #DC=6,# giving, #BC=BD+DC=4+6=10.#