Given here is a circle of a given radius. Inside it, three tangent circles of equal radius are inscribed. The task is to find the radii of these tangent circles.
Examples:
Input: R = 4
Output: 1.858Input: R = 11
Output: 5.1095
Approach:
Let the radii of the tangent circles be r, and the radius of the circumscribing circle
is R.x is the smaller distance from the circumference of the tangent circle and the center of the circumscribing circle.
From the diagram, it is very clear,
2r + x = R
- now in triangle OBC,
cos 30 = r/(r+x)
rcos30 + xcos30 = r
x = r(1-cos30)/cos30- also, x = R-2r
- So,
R-2r = r(1-cos30)/cos30
R-2r = 0.133r/0.867
R-2r = 0.153r
R = 2.153r
so, r = 0.4645RRadii of three tangent circles = 0.4645*radius of the circumscribed circle
Below is the implementation of the above approach:
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 <bits/stdc++.h>using namespace std;void threetangcircle(int R){ cout << "The radii of the tangent circles is " << 0.4645 * R << endl;}// Driver codeint 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 givenimport 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 givendef threetangcircle(R): print("The radii of the tangent", "circles is ", end="") print(0.4645 * R)# Driver codeR = 4threetangcircle(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 givenusing 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.. |
Javascript
<script>// javascript program to find the radii// of the three tangent circles// of equal radius when the radius// of the circumscribed circle is givenfunction threetangcircle(R){ document.write("The radii of the tangent circles is " + 0.4645 * R);}// Driver codevar R = 4;threetangcircle(R);// This code contributed by shikhasingrajput </script> |
PHP
<?php// PHP program to find the radii// of the three tangent circles// of equal radius when the radius// of the circumscribed circle is givenfunction threetangcircle($R){ echo "The radii of the tangent circles is ", ( 0.4645 * $R );}// Driver code$R = 4;threetangcircle($R); // This code is contributed by ihritik?> |
Output
The radii of the tangent circles is 1.858
Time Complexity: O(1)
Auxiliary Space: O(1)
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