# A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #(7pi)/8 #, and the triangle's area is #8 #. What is the area of the triangle's incircle?

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

[ A = rs ]

Where:

- A is the area of the incircle,
- r is the radius of the incircle,
- s is the semi-perimeter of the triangle.

To find the semi-perimeter (s) of the triangle, you add the lengths of its three sides and divide by 2:

[ s = \frac{{\text{Side 1} + \text{Side 2} + \text{Side 3}}}{2} ]

The lengths of the sides can be found using the law of cosines:

[ \text{Side} = \sqrt{a^2 + b^2 - 2ab\cos(\theta)} ]

Where:

- a and b are the lengths of two sides of the triangle,
- θ is the angle between those two sides.

Once you have the lengths of the sides and the semi-perimeter, you can use Heron's formula to find the area of the triangle:

[ A = \sqrt{s(s - \text{Side 1})(s - \text{Side 2})(s - \text{Side 3})} ]

After finding the area of the triangle, you can calculate the radius of the incircle using the formula mentioned earlier, and then multiply it by the semi-perimeter 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.

- A triangle has sides with lengths of 5, 2, and 3. What is the radius of the triangles inscribed circle?
- A triangle has corners at #(4 , 5 )#, #(1 ,3 )#, and #(5 ,3 )#. What is the radius of the triangle's inscribed circle?
- A circle has a chord that goes from #( 3 pi)/8 # to #(5 pi) / 3 # radians on the circle. If the area of the circle is #48 pi #, what is the length of the chord?
- How do you find the equation of a circle in standard form given C(5,6) and r=3?
- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/6 #, and the triangle's area is #45 #. What is the area of the triangle's incircle?

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