A triangle has corners at points A, B, and C. Side AB has a length of #18 #. The distance between the intersection of point A's angle bisector with side BC and point B is #3 #. If side AC has a length of #14 #, what is the length of side BC?

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Answer 1 · 2016-06-21T13:07:31

#BC=16/3~=5.33.#

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

Then by property of angle-bisector, we get #(BD)/(DC)=(AB)/(AC)#.

Here, putting, #AB=18, AC=14, BD=3#, we get, #3/(DC)=18/14#
#:. DC=3*14/18=7/3#

Hence, #BC=BD+DC=3+7/3=16/3~=5.33.#