# A triangle has corners at #(9 ,3 )#, #(4 ,9 )#, and #(2 ,8 )#. What is the area of the triangle's circumscribed circle?

61.34 approx

Radius R of the circumcircle of a triangle is given by the formula

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To find the area of the circumscribed circle of a triangle, you need to first calculate the circumradius ((R)) of the circle. Then, you can use the formula for the area of a circle ((A = \pi R^2)).

To find the circumradius ((R)), you can use the formula:

[R = \frac{abc}{4A}]

Where (a), (b), and (c) are the lengths of the sides of the triangle, and (A) is the area of the triangle.

The lengths of the sides of the triangle can be found using the distance formula between two points in the Cartesian plane:

[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}]

Once you have the lengths of the sides of the triangle, you can use Heron's formula to calculate the area ((A)) of the triangle:

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

Where (s) is the semi-perimeter of the triangle, calculated as:

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

After finding the area of the triangle ((A)), substitute it into the formula for the circumradius ((R)), and then use the formula for the area of a circle to find the area of the circumscribed circle.

This process will yield the area of the circumscribed circle of the given triangle.

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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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