A triangle has corners at points A, B, and C. Side AB has a length of 12 12. The distance between the intersection of point A's angle bisector with side BC and point B is 6 6. If side AC has a length of 8 8, what is the length of side BC?

1 Answer
Jim G.
Jan 30, 2017

BC=10" units"BC=10 units

Explanation:

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

"Then "BC=BD+CDThen BC=BD+CD

We know that BD = 6 and have to find CD

Using the color(blue)"angle bisector theorem"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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