# A triangle has corners at points A, B, and C. Side AB has a length of #26 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #14 #, what is the length of side BC?

Length of the side

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Using the Angle Bisector Theorem, we know that the ratio of the lengths of the two segments of the side divided by the length of the other side is equal.

Let x be the length of segment BC, and y be the length of the segment AC. Then, according to the theorem:

( \frac{AB}{BC} = \frac{AC}{BC} )

Given that AB = 26 and AC = 14, we have:

( \frac{26}{x} = \frac{14}{x + 9} )

Cross-multiplying, we get:

( 26(x + 9) = 14x )

Expanding and rearranging terms:

( 26x + 234 = 14x )

Subtracting 14x from both sides:

( 12x + 234 = 0 )

Subtracting 234 from both sides:

( 12x = -234 )

Dividing both sides by 12:

( x = -19.5 )

Since the length of a side cannot be negative, we discard this solution. Thus, there might be an error in the given data or problem setup.

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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 an area of #4 # and two sides of lengths #9 # and #3 #. Triangle B is similar to triangle A and has a side with a length of #32 #. What are the maximum and minimum possible areas of triangle B?
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