A triangle has corners at points A, B, and C. Side AB has a length of #21 #. The distance between the intersection of point A's angle bisector with side BC and point B is #7 #. If side AC has a length of #14 #, what is the length of side BC?

1 Answer
Jim G.
Feb 18, 2017

#BC=11 2/3" units"#

Explanation:

Let D be the point on BC where the angle bisector from A, intersects with BC

Then BC = BD + DC

We know BD = 7 and require to find DC.

Applying the #color(blue)"Angle bisector theorem"# to the triangle.

#color(red)(bar(ul(|color(white)(2/2)color(black)((AB)/(AC)=(BD)/(DC))color(white)(2/2)|)))#

substitute known values into the equation.

#rArr21/14=7/(DC)#

#color(blue)"cross multiply"#

#rArr21DC=7xx14#

#rArrDC=(7xx14)/21=14/3=4 2/3#

#rArrBC=7+4 2/3=11 2/3" units"#

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