A triangle has corners at points A, B, and C. Side AB has a length of #27 #. 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 #18 #, what is the length of side BC?

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Answer 1 · 2018-06-16T15:17:39

#color(blue)(BC= 45/2)#

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From the diagram:

The Bisector Theorem states:

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

We have:

#AC=18#

#DC=9#

#AB=27#

We need to find #|BD|#:

#:.#

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

#|BD|=(27*9)/18=27/2#

Therefore:

#|BC|=|BD|+|DC|=27/2+9=45/2#