# A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #pi/6 #, and the triangle's area is #18 #. What is the area of the triangle's incircle?

Area of the triangle's incircle is

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To find the area of the triangle's incircle, you can use the formula:

[ \text{Area of incircle} = \text{Semiperimeter of triangle} \times \text{Inradius} ]

The semiperimeter (( s )) of the triangle is calculated as the sum of the lengths of its sides divided by 2. The inradius (( r )) can be found using the formula:

[ r = \frac{A}{s} ]

Where ( A ) is the area of the triangle.

First, calculate the lengths of the sides of the triangle using the given angles and the Law of Sines. Then, find the semiperimeter and the inradius, and finally, use these values to find the area of the incircle.

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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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- A circle has a center at #(1 ,3 )# and passes through #(2 ,4 )#. What is the length of an arc covering #pi /4 # radians on the circle?
- Two circles have the following equations: #(x +2 )^2+(y -1 )^2= 49 # and #(x +4 )^2+(y +7 )^2= 25 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
- A circle has a chord that goes from #( 5 pi)/6 # to #(5 pi) / 4 # radians on the circle. If the area of the circle is #21 pi #, what is the length of the chord?
- A triangle has sides with lengths of 2, 3, and 8. What is the radius of the triangles inscribed circle?

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