# A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #(3pi)/4 #, and the triangle's area is #8 #. What is the area of the triangle's incircle?

The area of the incircle is

The area of the triangle is

The angle

The angle

The angle

The sine rule is

So,

Let the height of the triangle be

The area of the triangle is

But,

So,

Therefore,

The radius of the incircle is

The area of the incircle is

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To find the area of the triangle's incircle, we first need to calculate the semi-perimeter (( s )) of the triangle using the formula:

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

where ( a ), ( b ), and ( c ) are the lengths of the triangle's sides.

Then, we can use Heron's formula to find the area (( A )) of the triangle:

[ A = \sqrt{s(s - a)(s - b)(s - c)} ]

Next, we can use the formula for the radius (( r )) of the incircle of a triangle:

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

where ( A ) is the area of the triangle and ( s ) is the semi-perimeter.

Finally, we can find the area of the triangle's incircle using the formula for the area of a circle:

[ \text{Area of incircle} = \pi \cdot r^2 ]

Substitute the values obtained into the formula 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 circle has a chord that goes from #( pi)/6 # to #(7 pi) / 6 # radians on the circle. If the area of the circle is #135 pi #, what is the length of the chord?
- The central angle of a sector is 72° and the sector has an area of #5pi#. How do you find the radius?
- A circle has a chord that goes from #( pi)/4 # to #(13 pi) / 8 # radians on the circle. If the area of the circle is #27 pi #, what is the length of the chord?
- A triangle has corners at #(4 ,6 )#, #(2 ,9 )#, and #(8 ,4 )#. What is the area of the triangle's circumscribed circle?
- A circle has a center that falls on the line #y = 3/8x +8 # and passes through # ( 7 ,4 )# and #(2 ,9 )#. What is the equation of the circle?

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