内接在给定半径的圆内的三个等半径的切圆的半径

这里给出的是一个给定半径的圆。在其内部，内接三个等半径的切圆。任务是找到这些切圆的半径。
例子：

Input: R = 4
Output: 1.858

Input: R = 11
Output:: 5.1095

方法：

• 设切圆的半径为r ，外接圆的半径为
  是R 。 x是到切圆圆周和外接圆中心的较小距离。
• 从图中可以很清楚地看出，
  2r + x = R
• 现在在三角形OBC 中，
  cos 30 = r/(r+x)
  rcos30 + xcos30 = r
  x = r(1-cos30)/cos30
• 同样， x = R-2r
• 所以，
  R-2r = r(1-cos30)/cos30
  R-2r = 0.133r/0.867
  R-2r = 0.153r
  R = 2.153r
  所以， r = 0.4645R

$Radii of three tangent circles = 0.4645*radius of the circumscribed circle$

C++

// C++ program to find the radii
// of the three tangent circles
// of equal radius when the radius
// of the circumscribed circle is given
 
#include 
using namespace std;
 
void threetangcircle(int R)
{
    cout << "The radii of the tangent circles is "
         << 0.4645 * R << endl;
}
 
// Driver code
int main()
{
    int R = 4;
    threetangcircle(R);
    return 0;
}
Java // Java program to find the radii
// of the three tangent circles
// of equal radius when the radius
// of the circumscribed circle is given
import java.io.*;

class GFG 
{

static void threetangcircle(int R)
{
    System.out.print("The radii of the tangent circles is "
        + 0.4645 * R);
}

// Driver code
public static void main (String[] args) 
{
    int R = 4;
    threetangcircle(R);
}
}

// This code is contributed by anuj_67..

Python3

# Python3 program to find the radii
# of the three tangent circles
# of equal radius when the radius
# of the circumscribed circle is given
 
def threetangcircle(R):
    print("The radii of the tangent",
          "circles is ", end = "");
    print(0.4645 * R);
 
# Driver code
R = 4;
threetangcircle(R);
 
# This code is contributed
# by Princi Singh

C#

// C# program to find the radii
// of the three tangent circles
// of equal radius when the radius
// of the circumscribed circle is given
using System;
 
class GFG
{
 
static void threetangcircle(int R)
{
    Console.WriteLine("The radii of the tangent circles is "
        + 0.4645 * R);
}
 
// Driver code
public static void Main ()
{
    int R = 4;
    threetangcircle(R);
}
}
 
// This code is contributed by anuj_67..
PHP 

Javascript

// javascript program to find the radii
// of the three tangent circles
// of equal radius when the radius
// of the circumscribed circle is given
 
function threetangcircle(R)
{
    document.write("The radii of the tangent circles is "
        + 0.4645 * R);
}
 
// Driver code
var R = 4;
threetangcircle(R);
 
 
// This code contributed by shikhasingrajput

输出：

The radii of the tangent circles is 1.858

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