# A triangle has vertices A, B, and C. Vertex A has an angle of #pi/8 #, vertex B has an angle of #( pi)/4 #, 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 incircle of the triangle, we can use the formula:

[ A = rs ]

Where:

- ( A ) is the area of the triangle
- ( r ) is the radius of the incircle
- ( s ) is the semi-perimeter of the triangle

The semi-perimeter ( s ) can be calculated as:

[ s = \frac{a + b + c}{2} ]

Where ( a ), ( b ), and ( c ) are the side lengths of the triangle.

Using the given angles, we can calculate the side lengths of the triangle using trigonometric ratios. Then, we can find the semi-perimeter and use it to calculate the radius of the incircle. Finally, we use the formula ( A = \pi r^2 ) 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.

- Find the equation to the circle which touches y-axis at the origin and passes though the point (alpha,beta)?
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- A triangle has corners at #(2 , 6 )#, #(3 ,9 )#, and #(4 ,5 )#. What is the radius of the triangle's inscribed circle?
- A circle has a chord that goes from #( 3 pi)/2 # to #(7 pi) / 4 # radians on the circle. If the area of the circle is #121 pi #, what is the length of the chord?
- Two circles have the following equations #(x +2 )^2+(y -5 )^2= 16 # and #(x +4 )^2+(y +1 )^2= 49 #. 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?

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