# A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #(5pi)/12 #, and the triangle's area is #18 #. 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 triangle's semiperimeter, ( s ), 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 of the triangle, which is given by:

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

Once we have the triangle's semiperimeter and area, we can use the formula for the radius (( r )) of the incircle, which is given by:

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

Finally, the area of the incircle (( A_{\text{incircle}} )) is calculated using the formula for the area of a circle:

[ A_{\text{incircle}} = \pi r^2 ]

We can substitute the values we have into these formulas to find the area of the triangle's 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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- How do you find an equation of the circle having center (4,-3) and radius 5?

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