# A triangle has corners at #(7 ,8 )#, #(2 ,3 )#, and #(1 ,4 )#. What is the area of the triangle's circumscribed circle?

Area of the circle = 1.2752

By signing up, you agree to our Terms of Service and Privacy Policy

To find the area of the circumscribed circle of a triangle, we need to find the circumradius, which is the radius of the circle passing through all three vertices of the triangle.

First, calculate the lengths of the sides of the triangle using the distance formula. Then, use Heron's formula to find the area of the triangle. Finally, use the formula ( A = \frac{{abc}}{{4R}} ), where ( A ) is the area of the triangle, ( a ), ( b ), and ( c ) are the lengths of its sides, and ( R ) is the circumradius.

After finding the area of the triangle and the lengths of its sides, solve for the circumradius using the given formula. Once you have the circumradius, you can find the area of the circumscribed circle using the formula for the area of a circle (( A = \pi R^2 )).

Given the coordinates of the triangle's vertices, you can follow these steps to calculate the area of the circumscribed circle.

By signing up, you agree to our Terms of Service and Privacy Policy

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 triangle has corners at #(6 ,3 )#, #(5 ,4 )#, and #(3 ,2 )#. What is the area of the triangle's circumscribed circle?
- What is the equation of the circle with a center at #(-1 ,-3 )# and a radius of #7 #?
- A circle's center is at #(3 ,9 )# and it passes through #(4 ,5 )#. What is the length of an arc covering #( pi ) /6 # radians on the circle?
- A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length of an arc covering #pi # radians on the circle?
- A triangle has sides with lengths of 8, 7, and 6. What is the radius of the triangles inscribed circle?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7