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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 #6 #. If side AC has a length of #8 #, what is the length of side BC?

Answer 1

Mason Adams

#BC=10" units"#

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

#"Then "BC=BD+CD#

We know that BD = 6 and have to find CD

Using the #color(blue)"angle bisector theorem"#

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

Substitute known values into this equation and solve for CD

#rArr6/(CD)=12/8#

#color(blue)"cross multiplying"#

#rArr12CD=6xx8#

#rArrCD=48/12=4#

#rArrBC=6+4=10" units"#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.