# A triangle has corners at #(2 ,8 )#, #(3 ,9 )#, and #(4 ,7 )#. What is the area of the triangle's circumscribed circle?

And the same for equations [1] and [3]:

The square terms cancel:

Collect all of the constant terms on the left:

Collect all the h terms on the right:

Collect all of the k terms on the left:

Divide equation 4 by 2 and equation 5 by -2:

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

(Area = \frac{abc}{4R})

Where (a), (b), and (c) are the lengths of the sides of the triangle, and (R) is the radius of the circumscribed circle.

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

(a = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2})

(b = \sqrt{(x_3 - x_2)^2 + (y_3 - y_2)^2})

(c = \sqrt{(x_3 - x_1)^2 + (y_3 - y_1)^2})

Then, use Heron's formula to find the area of the triangle:

(s = \frac{a + b + c}{2})

(Area_{triangle} = \sqrt{s(s - a)(s - b)(s - c)})

Once you have the area of the triangle, you can find the radius of the circumscribed circle using the formula:

(R = \frac{abc}{4Area_{triangle}})

Finally, plug in the values to find the area of the circumscribed circle using the formula:

(Area_{circle} = \pi R^2)

Calculating these values will give you the area of the triangle's circumscribed circle.

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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 #( 5 pi)/4 # to #(4 pi) / 3 # radians on the circle. If the area of the circle is #64 pi #, what is the length of the chord?
- How do you write an equation of a circle with center (3,0) passes through the point (-2,4)?
- A circle has a center that falls on the line #y = 2/3x +7 # and passes through #(5 ,7 )# and #(1 ,2 )#. What is the equation of the circle?
- Two circles have the following equations: #(x -1 )^2+(y -4 )^2= 64 # and #(x +6 )^2+(y -9 )^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?
- A circle has a center that falls on the line #y = 2/9x +4 # and passes through # ( 3 ,1 )# and #(5 ,7 )#. What is the equation of the circle?

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