A triangle has corners at points A, B, and C. Side AB has a length of #7 #. The distance between the intersection of point A's angle bisector with side BC and point B is #6 #. If side AC has a length of #14 #, what is the length of side BC?

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Answer 1 · 2017-11-29T13:45:06

#BC = 18#

As per the angular bisector theorem,
#|BD|/|DC| = |AB|/|AC|#
D is point on side BC where the angular bisector of #/_A # meets.

Given AB = 7, AC = 14 and BD = 6.

#:.6/(DC) = 7/14#

#DC = (14/7)*6 = 12#

#BC = BD + DC = 6 + 12 = 18#