# A triangle has corners at 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 #21 #, what is the length of side BC?

Length of side BC = 20

Let the point where the angle bisector intersects with side BC be D

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Using the Angle Bisector Theorem, we can find the length of side BC. The theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides.

Given that the length of side AB is 9, and the distance between the intersection of point A's angle bisector with side BC and point B is 6, we can set up the following proportion:

[ \frac{AC}{AB} = \frac{BC}{6} ]

Substituting the given values, we have:

[ \frac{21}{9} = \frac{BC}{6} ]

Solving for BC:

[ BC = \frac{21}{9} \times 6 ] [ BC = 14 ]

Therefore, the length of side BC is 14.

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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.

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- Triangle A has sides of lengths #12 ,1 4#, and #11 #. Triangle B is similar to triangle A and has a side of length #9 #. What are the possible lengths of the other two sides of triangle B?

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