A triangle has corners at points A, B, and C. Side AB has a length of #16 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #19 #, what is the length of side BC?

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Answer 1 · 2017-01-25T07:14:00

#bar(BC)=17.5#

Let D be the intersection of point A's bisector with side BC, then

#bar(BD)=8#.

By the bisector theorem, it is:

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

Then #CD=(AC*BD)/(AB)#

that's

#bar(CD)=(19*8)/16=9.5#

Since #BC=BD+CD#, you get

#bar(BC)=8+9.5=17.5#