A triangle has corners at 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 #8 #. If side AC has a length of #27 #, what is the length of side BC?

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Answer 1 · 2017-01-30T06:24:16

The length of side BC is 26

Let D be the intersection of point A's angle bisector with side BC.

Then #BD=8#

The bisector theorem states that:

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

Then

#27/12=(CD)/8#

that's

#CD=(27*8)/12=18#

Then #BC=CD+BD=8+18=26#