# A triangle has corners at points A, B, and C. Side AB has a length of #16 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #19 #, what is the length of side BC?

Let D be the intersection of point A's bisector with side BC, then

By the bisector theorem, it is:

that's

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The length of side BC is 20.

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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.

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.

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.

- Triangle A has an area of #8 # and two sides of lengths #5 # and #9 #. Triangle B is similar to triangle A and has a side of length #12 #. What are the maximum and minimum possible areas of triangle B?
- Triangle A has an area of #18 # and two sides of lengths #8 # and #12 #. Triangle B is similar to triangle A and has a side of length #8 #. What are the maximum and minimum possible areas of triangle B?
- A triangle has corners points A, B, and C. Side AB has a length of #5 #. The distance between the intersection of point A's angle bisector with side BC and point B is #3 #. If side AC has a length of #4 #, what is the length of side BC?
- 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?
- The sides of a triangle are 5, 6 and 10. How do you find the length of the longest side of a similar triangle whose shortest side is 15?

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