Question

A triangle has corners 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 `10`, what is the length of side BC?

Answer 1

Side `BC=12 2/3=12.6666" "`units

Explanation:

There is a theorem in Geometry which states ,"An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle."

Let the intersection be point `I`

Therefore, our equation is as follows
`AB:IB=AC:IC`

`(AB)/(IB)=(AC)/(IC)`

`9/6=10/(IC)`

`IC=(6(10))/9`

`IC=20/3`

The length of `BC=IB+IC`

`BC=6+20/3`

`BC=38/3=12 2/3`

God bless...I hope the explanation is useful.