给定等边三角形M的中位数,任务是使用中位数 M 找到该等边三角形的外接圆面积。
例子:
Input: M = 3
Output: 12.5664
Input: M = 6
Output: 50.2655
方法:问题中的关键观察是等边三角形的质心、外心、垂心和内心都在同一点上。
因此,内接等边三角形的给定中值的圆的半径可以推导出为:
然后可以使用本文中使用的方法计算圆的面积
下面是上述方法的实现:
C++
// C++ implementation to find the
// equation of circle which
// inscribes equilateral triangle
// of median M
#include
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
输出:
12.5664