The Circumscribed Circle Calculator is a tool used to determine the radius of the circumscribed circle for a given triangle or polygon. This radius indicates the distance from the center of the circle to its outer boundary that just touches all the vertices of the shape.
Formula of Circumscribed Circle Calculator
In general, the formula to calculate the radius (R) of the circumscribed circle is:
R=a×b×c / 4×A
Where:
- R represents the radius of the circumscribed circle.
- a, b, and c denote the lengths of the sides of the triangle or polygon.
- A signifies the area of the triangle or polygon.
General Terms
Here are some common terms and related phrases that users often search for while utilizing the Circumscribed Circle Calculator:
| Term | Description |
|---|---|
| Circumscribed Circle Radius | The distance from the center to the outer edge of the circle that encompasses all vertices of the shape. |
| Triangle | A polygon with three sides and three angles. |
| Polygon | A closed figure with three or more straight sides. |
| Circumscribed | The circle that passes through all the vertices of the shape. |
This table aims to assist users by offering a quick reference for terms commonly associated with the Circumscribed Circle Calculator.
Example of Circumscribed Circle Calculator
Consider a triangle with side lengths: a = 3 units, b = 4 units, and c = 5 units. To determine the circumscribed circle's radius:
R=a×b×c / 4×A
A=s×(s−a)×(s−b)×(s−c) where s=a+b+c / 2
Given that s=3+4+5 / 2=6 units, A=6×(6−3)×(6−4)×(6−5)=6×3×2×1=36=6 square units.
Thus, R=3×4×5 / 4×6=2460=2.5 units.
Most Common FAQs
A: The Circumscribed Circle is a circle that passes through all the vertices of a given polygon or triangle.
A: Simply input the lengths of the sides of your triangle or polygon into the calculator, then click 'Calculate' to find the radius of the circle.
A: The Circumscribed Circle plays a significant role in geometry, especially in determining certain properties of polygons and triangles, aiding in various mathematical and engineering applications.