# A triangle has corners at #(4 ,6 )#, #(2 ,9 )#, and #(7 ,5 )#. What is the area of the triangle's circumscribed circle?

The area of the triangle's circumscribed circle

Let

Using Distance formula ,we get

Using cosine Formula ,we get

We know that,

Using sine formula:we get

So , the area of the triangle's circumscribed circle is:

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

Area = (abc) / (4 * radius)

where a, b, and c are the lengths of the sides of the triangle, and radius is the radius of the circumscribed circle.

First, calculate the lengths of the sides using the distance formula:

Side a: √((4 - 2)^2 + (6 - 9)^2) Side b: √((2 - 7)^2 + (9 - 5)^2) Side c: √((7 - 4)^2 + (5 - 6)^2)

Then, calculate the semi-perimeter (s) of the triangle:

s = (a + b + c) / 2

Next, calculate the area of the triangle using Heron's formula:

Area_triangle = √(s * (s - a) * (s - b) * (s - c))

Finally, use the formula for the area of the circle:

Area_circle = π * radius^2

where the radius of the circumscribed circle can be found using the formula:

radius = (a * b * c) / (4 * Area_triangle)

Calculate the area of the circle using the radius obtained.

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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 with a radius of 6 meters has an arc that measures 35. If this arc and its associated sector are completely removed from the circle, what is the length of the major arc that remains, to the nearest tenth of a meter?
- 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 #18 #. What is the area of the triangle's incircle?

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