Given two circles, of given radii, have there centres a given distance apart, such that the circles don’t touch each other. The task is to find the length of the direct common tangent between the circles.
Examples:
Input: r1 = 4, r2 = 6, d = 12 Output: 11.8322 Input: r1 = 5, r2 = 9, d = 25 Output: 24.6779
Approach:
- Let the radii of the circles be r1 & r2 respectively.
- Let the distance between the centers be d units.
- Draw a line OR parallel to PQ
- angle OPQ = 90 deg
angle O’QP = 90 deg
{ line joining the centre of the circle to the point of contact makes an angle of 90 degrees with the tangent } - angle OPQ + angle O’QP = 180 deg
OP || QR - Since opposite sides are parallel and interior angles are 90, therefore OPQR is a rectangle.
- So OP = QR = r1 and PQ = OR = d
- In triangle OO’R
angle ORO’ = 90
By Pythagoras theorem
OR^2 + O’R^2 = (OO’^2)
OR^2 + (r1-r2)^2 = d^2 - so, OR^2= d^2-(r1-r2)^2
OR = ?{d^2-(r1-r2)^2}
Below is the implementation of the above approach:
C++
// C++ program to find// the length of the direct// common tangent between two circles// which donot touch each other#include <bits/stdc++.h>using namespace std;// Function to find the length of the direct common tangentvoid lengtang(double r1, double r2, double d){ cout << "The length of the direct" <<" common tangent is " << sqrt(pow(d, 2) - pow((r1 - r2), 2)) << endl;}// Driver codeint main(){ double r1 = 4, r2 = 6, d = 12; lengtang(r1, r2, d); return 0;} |
Java
// Java program to find// the length of the direct// common tangent between two circles// which donot touch each otherclass GFG{// Function to find the length of// the direct common tangentstatic void lengtang(double r1, double r2, double d){ System.out.println("The length of the direct" +" common tangent is " +(Math.sqrt(Math.pow(d, 2) - Math.pow((r1 - r2), 2))));}// Driver codepublic static void main(String[] args){ double r1 = 4, r2 = 6, d = 12; lengtang(r1, r2, d);}}/* This code contributed by PrinciRaj1992 */ |
Python3
# Python3 program to find# the length of the direct# common tangent between two circles# which do not touch each otherimport math# Function to find the length# of the direct common tangentdef lengtang(r1, r2, d): print("The length of the direct common tangent is", (((d ** 2) - ((r1 - r2) ** 2)) ** (1 / 2)));# Driver coder1 = 4; r2 = 6; d = 12;lengtang(r1, r2, d);# This code is contributed by 29AjayKumar |
C#
// C# program to find// the length of the direct// common tangent between two circles// which donot touch each otherusing System;class GFG{ // Function to find the length of // the direct common tangent static void lengtang(double r1, double r2, double d) { Console.WriteLine("The length of the direct" +" common tangent is " +(Math.Sqrt(Math.Pow(d, 2) - Math.Pow((r1 - r2), 2)))); } // Driver code public static void Main() { double r1 = 4, r2 = 6, d = 12; lengtang(r1, r2, d); }}// This code is contributed by AnkitRai01 |
PHP
<?php// PHP program to find the length// of the direct common tangent// between two circles which// donot touch each other// Function to find the length// of the direct common tangentfunction lengtang($r1, $r2, $d){ echo "The length of the direct", " common tangent is ", sqrt(pow($d, 2) - pow(($r1 - $r2), 2)), "\n";}// Driver code$r1 = 4;$r2 = 6;$d = 12;lengtang($r1, $r2, $d);// This code is contributed by akt_mit?> |
Javascript
<script>// Javascript program to find// the length of the direct// common tangent between two circles// which donot touch each other// Function to find the length of the direct common tangentfunction lengtang(r1, r2, d){ document.write("The length of the direct common tangent is "+ Math.sqrt(Math.pow(d, 2) - Math.pow((r1 - r2), 2)));}// Driver code var r1 = 4, r2 = 6, d = 12; lengtang(r1, r2, d);</script> |
Output:
The length of the direct common tangent is 11.8322
Time Complexity: O(1)
Auxiliary Space: O(1)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
