# 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 #15 #, what is the length of side BC?

According to angle bisector theorem,

Given

Hence,

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Using the Angle Bisector Theorem, we can find the length of side BC.

Let D be the point where the angle bisector of angle A intersects side BC. According to the Angle Bisector Theorem, BD/DC = AB/AC.

Given that AB = 9 and AC = 15, we have: BD/DC = 9/15 = 3/5.

Let x be the length of BD, then DC = 5x/3.

Also, given that the distance between D and B is 6 units, we have: DB + DC = 6 x + 5x/3 = 6 Multiplying both sides by 3 to clear the fraction: 3x + 5x = 18 8x = 18 x = 18/8 = 9/4

Thus, the length of BD is 9/4 units.

To find the length of BC, we add BD and DC: BC = BD + DC BC = 9/4 + 5(9/4)/3 BC = 9/4 + 15/4 BC = 24/4 BC = 6 units.

So, the length of side BC is 6 units.

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The length of side BC is 18.

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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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