# Area of Circumcircle of an Equilateral Triangle using Median

Given the median of the Equilateral triangle **M**, the task is to find the area of the circumcircle of this equilateral triangle using the median M.

**Examples:**

Input:M = 3Output:12.5664

Input:M = 6Output:50.2655

**Approach:** The key observation in the problem is that the centroid, circumcenter, orthocenter and incenter of an equilateral triangle all lie at the same point.

Therefore, the radius of the circle with the given median of the equilateral triangle inscribed in the circle can be derived as:

Then the area of the circle can be calculated using the approach used in this article

Below is the implementation of the above approach:

## C++

`// C++ implementation to find the` `// equation of circle which` `// inscribes equilateral triangle` `// of median M` `#include <iostream>` `const` `double` `pi = 3.14159265358979323846;` `using` `namespace` `std;` `// Function to find the equation` `// of circle whose center is (x1, y1)` `// and the radius of circle is r` `void` `circleArea(` `double` `r)` `{` ` ` `cout << (pi * r * r);` `}` `// Function to find the` `// equation of circle which` `// inscribes equilateral triangle` `// of median M` `void` `findCircleAreaByMedian(` `double` `m)` `{` ` ` `double` `r = 2 * m / 3;` ` ` `// Util Function to find the` ` ` `// circle equation` ` ` `circleArea(r);` `}` `// Driver code` `int` `main()` `{` ` ` `double` `m = 3;` ` ` `// Function Call` ` ` `findCircleAreaByMedian(m);` ` ` `return` `0;` `}` |

## Java

`// Java implementation to find the` `// equation of circle which` `// inscribes equilateral triangle` `// of median M` `import` `java.util.*;` `class` `GFG{` ` ` `// Function to find the equation` `// of circle whose center is (x1, y1)` `// and the radius of circle is r` `static` `double` `circleArea(` `double` `r)` `{` ` ` `double` `pi = ` `3.14159265358979323846` `;` ` ` `return` `(pi * r * r);` `}` ` ` `// Function to find the` `// equation of circle which` `// inscribes equilateral triangle` `// of median M` `static` `double` `findCircleAreaByMedian(` `int` `m)` `{` ` ` `double` `r = ` `2` `* m / ` `3` `;` ` ` ` ` `// Function call to find` ` ` `// the circle equation` ` ` `return` `circleArea(r);` `}` `// Driver code` `public` `static` `void` `main(String args[])` `{` ` ` `int` `m = ` `3` `;` ` ` ` ` `System.out.printf(` `"%.4f"` `, findCircleAreaByMedian(m));` `}` `}` `// This code is contributed by virusbuddah_` |

## Python3

`# Python3 implementation to find the` `# equation of circle which inscribes` `# equilateral triangle of median M` `pi ` `=` `3.14159265358979323846` `# Function to find the equation` `# of circle whose center is (x1, y1)` `# and the radius of circle is r` `def` `circleArea(r):` ` ` ` ` `print` `(` `round` `(pi ` `*` `r ` `*` `r, ` `4` `))` `# Function to find the` `# equation of circle which` `# inscribes equilateral triangle` `# of median M` `def` `findCircleAreaByMedian(m):` ` ` ` ` `r ` `=` `2` `*` `m ` `/` `3` ` ` `# Function to find the` ` ` `# circle equation` ` ` `circleArea(r)` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `m ` `=` `3` ` ` `# Function call` ` ` `findCircleAreaByMedian(m)` `# This code is contributed by mohit kumar 29` |

## C#

`// C# implementation to find the` `// equation of circle which` `// inscribes equilateral triangle` `// of median M` `using` `System;` `class` `GFG{` ` ` `// Function to find the equation` `// of circle whose center is (x1, y1)` `// and the radius of circle is r` `static` `double` `circleArea(` `double` `r)` `{` ` ` `double` `pi = 3.14159265358979323846;` ` ` `return` `(pi * r * r);` `}` ` ` `// Function to find the` `// equation of circle which` `// inscribes equilateral triangle` `// of median M` `static` `double` `findCircleAreaByMedian(` `int` `m)` `{` ` ` `double` `r = 2 * m / 3;` ` ` ` ` `// Function call to find` ` ` `// the circle equation` ` ` `return` `circleArea(r);` `}` ` ` `// Driver code` `public` `static` `void` `Main(` `string` `[]args)` `{` ` ` `int` `m = 3;` ` ` ` ` `Console.WriteLine(` `"{0:f4}"` `, findCircleAreaByMedian(m));` `}` `}` `// This code is contributed by AnkitRai01` |

## Javascript

`<script>` `// javascript implementation to find the` `// equation of circle which` `// inscribes equilateral triangle` `// of median M` ` ` `// Function to find the equation` ` ` `// of circle whose center is (x1, y1)` ` ` `// and the radius of circle is r` ` ` `function` `circleArea(r) {` ` ` `var` `pi = 3.14159265358979323846;` ` ` `return` `(pi * r * r);` ` ` `}` ` ` `// Function to find the` ` ` `// equation of circle which` ` ` `// inscribes equilateral triangle` ` ` `// of median M` ` ` `function` `findCircleAreaByMedian(m) {` ` ` `var` `r = 2 * m / 3;` ` ` `// Function call to find` ` ` `// the circle equation` ` ` `return` `circleArea(r);` ` ` `}` ` ` `// Driver code` ` ` ` ` `var` `m = 3;` ` ` `document.write(findCircleAreaByMedian(m).toFixed(4));` `// This code is contributed by Rajput-Ji` `</script>` |

**Output**

12.5664

**Time Complexity: **O(1), as we are not using any looping statements.**Auxiliary Space: **O(1), as we are not using any extra space.