A triangle has corners at points A, B, and C. Side AB has a length of #10 #. The distance between the intersection of point A's angle bisector with side BC and point B is #2 #. If side AC has a length of #8 #, what is the length of side BC?

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Answer 1 · 2016-04-03T04:30:55

#bc=4#

Consider the diagram

enter image source here

Always remember that the angle bisector of any angle in a triangle also bisects the opposite side into two equal halves

So,

We can say that

#color(purple)(bd=dc#

#rarr2=2#

So,the length of

#color(green)(bc=bd+dc=2+2=4#