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Find the radii of the circles which are lined in a row, and distance between the centers of first and last circle is given
  • Last Updated : 22 Mar, 2021

Given here are n circles which touch each other externally, and are lined up in a row. The distance between the centers of the first and last circle is given. The circles have a radius of equal length. The task is to find the radius of each circle. 
Examples: 
 

Input: d = 42, n = 4
Output: The radius of each circle is 7

Input: d = 64, n = 5
Output: The radius of each circle is 8

 

Approach
Suppose there are n circles each having radius of length r
Let, the distance between the first and last circles = d 
From the figure, it is clear, 
r + r + (n-2)*2r = d 
2r + 2nr – 4r = d 
2nr – 2r = d 
so, r = d/(2n-2)
The radius of each circle = distance between the first and last circles/(2*no.of circles -2)
 

C++




// C++ program to find radii of the circles
// which are lined in a row
// and distance between the
// centers of first and last circle is given
 
#include <bits/stdc++.h>
using namespace std;
 
void radius(int n, int d)
{
    cout << "The radius of each circle is "
         << d / (2 * n - 2) << endl;
}
 
// Driver code
int main()
{
    int d = 42, n = 4;
    radius(n, d);
    return 0;
}

Java




// Java program to find radii of the circles
// which are lined in a row
// and distance between the
// centers of first and last circle is given
import java.io.*;
 
class GFG
{
 
static void radius(int n, int d)
{
    System.out.print( "The radius of each circle is "
        +d / (2 * n - 2));
}
 
// Driver code
static public void main (String []args)
{
    int d = 42, n = 4;
    radius(n, d);
}
}
 
// This code is contributed by anuj_67..

Python3




# Python program to find radii of the circles
# which are lined in a row
# and distance between the
# centers of first and last circle is given
 
def radius(n, d):
    print("The radius of each circle is ",
        d / (2 * n - 2));
 
d = 42; n = 4;
radius(n, d);
 
 
# This code is contributed by PrinciRaj1992

C#




// C# program to find radii of the circles
// which are lined in a row
// and distance between the
// centers of first and last circle is given
using System;
 
class GFG
{
 
static void radius(int n, int d)
{
    Console.Write( "The radius of each circle is "
        +d / (2 * n - 2));
}
 
// Driver code
static public void Main ()
{
    int d = 42, n = 4;
    radius(n, d);
}
}
 
// This code is contributed by anuj_67..

Javascript




<script>
// javascript program to find radii of the circles
// which are lined in a row
// and distance between the
// centers of first and last circle is given
function radius(n , d)
{
    document.write( "The radius of each circle is "
        +d / (2 * n - 2));
}
 
// Driver code
var d = 42, n = 4;
radius(n, d);
 
// This code is contributed by 29AjayKumar
</script>
Output: 
The radius of each circle is 7

 

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