# A triangle has corners at points A, B, and C. Side AB has a length of #18 #. 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 #20 #, what is the length of side BC?

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Length of

Given : side AB = c = 18, BD = 3 & AC = 20.

To find BC.

As per angular bisector theorem,

But

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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 (AB = 18) and (AC = 20), we can substitute these values:

(BD/DC = 18/20)

(BD/DC = 9/10)

Given that (BD + DC = BC), and we know (BD) (3) and the ratio (BD/DC), we can solve for (BC).

(3 + 3x = BC), where (x) represents the common multiplier for (BD) and (DC), found from the ratio (9/10).

Solving for (x):

(3x = BC - 3)

(3x = BC - 3)

(x = (BC - 3)/3)

From the ratio (BD/DC = 9/10), we have (BD = 3), (DC = 3x), and (BD/DC = 9/10).

Substituting the values:

(3 / (3x) = 9/10)

Solving for (x):

(x = 10/3)

Substitute (x) back into the equation for (BC):

(BC = 3 + 3(10/3))

(BC = 3 + 10)

(BC = 13)

So, the length of side BC is 13.

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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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