# A triangle has corners at points A, B, and C. Side AB has a length of #6 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #8 #, what is the length of side BC?

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Using the Angle Bisector Theorem, we can find the length of side BC. According to the theorem, the ratio of the lengths of the segments formed by the angle bisector of a triangle is equal to the ratio of the lengths of the sides of the triangle.

Let D be the point where the angle bisector of angle A intersects side BC.

Using the given information: AD/DB = AC/CB

Substituting the given values: (4 + x) / (6 - x) = 8 / 6

Cross multiplying: 8(6 - x) = 6(4 + x)

Expanding and simplifying: 48 - 8x = 24 + 6x

Bringing like terms to one side: 48 - 24 = 8x + 6x 24 = 14x

Dividing both sides by 14: x = 24 / 14 x = 12 / 7

So, the length of side BC is: BC = 6 - x BC = 6 - 12/7 BC = (42 - 12) / 7 BC = 30 / 7

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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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