A triangle has corners at points A, B, and C. Side AB has a length of #9 #. 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 #16 #, what is the length of side BC?
1 Answer
Apr 6, 2017
Explanation:
Let D be the point on BC where the angle bisector intersects BC.
#rArrBC=BD+DC# We are given BD = 6 and require to find DC
#"Using the "color(blue)" Angle bisector theorem"#
#color(red)(bar(ul(|color(white)(2/2)color(black)((AB)/(AC)=(BD)/(DC))color(white)(2/2)|)))# Substitute given values into this equation.
#9/16=6/(DC)#
#color(blue)"cross-multiply"#
#9xxDC=6xx16#
#rArrDC=(6xx16)/9=32/3#
#rArrBC=6+32/3=16 2/3" units"#
