# Circumscribed Circle of a Triangle Calculator

Calculate the properties of the circumscribed circle around a triangle with ease using our calculator.

## Similar Calculators:

- Segment of Circle Calculator
- Trapezoid Calculator with Angles
- Ultimate Triangle Calculator
- Ultimate Regular Polygons Calculator
**More Math Calculators**

The circumcircle of a triangle is a circle that passes through all three vertices of the triangle. It is a unique circle that can be constructed using various methods, including the intersection of perpendicular bisectors of the triangle’s sides. The circumcircle is an essential concept in geometry and has many applications in fields such as architecture, engineering, and computer graphics.

## The Importance of the Circumscribed Circle

The circumcircle of a triangle plays a crucial role in understanding the properties and relationships of triangles. By studying the circumcircle, we can derive valuable information about the triangle, such as its radius, area, and angles. This knowledge is not only fundamental in geometry but also has practical applications in real-world scenarios, such as calculating the dimensions of circular objects or designing structures with triangular components.

## The Formula for Calculating the Circumcircle Radius

To calculate the radius of the circumcircle of a triangle, we can use the following formula:

\[ R = \frac{abc}{4\sqrt{s(s-a)(s-b)(s-c)}} \]

where ( a ), ( b ), and ( c ) are the lengths of the triangle’s sides, and ( s ) is the semiperimeter given by ( s = \frac{a+b+c}{2} ). This formula allows us to determine the radius of the circumcircle using only the side lengths of the triangle.

## Using the Circumscribed Circle of a Triangle Calculator

The Circumscribed Circle of a Triangle Calculator simplifies the process of calculating the radius and other properties of the circumcircle. To use the calculator effectively, follow these steps:

- Enter the lengths of the triangle’s sides, denoted as ( a ), ( b ), and ( c ).
- Press the
**“Calculate”**button to obtain the radius of the circumcircle. - The calculator will display the radius, as well as other useful information such as the area of the triangle and the area ratio between the circumcircle and the triangle.

## Example Calculation

Let’s consider an example to illustrate the use of the Circumscribed Circle of a Triangle Calculator. Suppose we have a triangle with side lengths of 6, 7, and 10. By entering these values into the calculator, we can determine the radius of the circumcircle.

Using the formula mentioned earlier, we can calculate the radius as follows:

\[ R = \frac{6 \cdot 7 \cdot 10}{4\sqrt{(11.5)(11.5-6)(11.5-7)(11.5-10)}} \]

After performing the calculation, we find that the radius of the circumcircle is approximately 5.08.

The Circumscribed Circle of a Triangle Calculator is an invaluable tool for anyone studying or working with triangles and circles. By using this calculator, you can effortlessly determine the radius and other properties of the circumcircle, gaining insights into the relationships and characteristics of triangles. With its user-friendly interface and additional resources, the calculator provides a comprehensive solution for all your circumcircle calculations. Harness the power of the Circumscribed Circle of a Triangle Calculator to unlock the potential of geometry and explore the fascinating world of triangles and their circumcircles.