Shortest distance from the centre of a circle to a chord
Given a circle which has a chord inside it. The length of the chord and the radius of the circle are given. The task is to find the shortest distance from the chord to the centre.
Examples:
Input: r = 4, d = 3 Output: 3.7081 Input: r = 9.8, d = 7.3 Output: 9.09492
Approach:
from pythagorus theorem,
OB^2 + (d/2)^2 = r^2
so, OB = √(r^2 – d^2/4)

Below is the implementation of the above approach:
C++
// C++ program to find // the shortest distance from // chord to the centre of circle #include <bits/stdc++.h> using namespace std; // Function to find the shortest distance void shortdis( double r, double d) { cout << "The shortest distance " << "from the chord to centre " << sqrt ((r * r) - ((d * d) / 4)) << endl; } // Driver code int main() { double r = 4, d = 3; shortdis(r, d); return 0; } |
Java
// Java program to find // the shortest distance from // chord to the centre of circle class GFG { // Function to find the shortest distance static void shortdis( double r, double d) { System.out.println( "The shortest distance " + "from the chord to centre " + (Math.sqrt((r * r) - ((d * d) / 4 )))); } // Driver code public static void main(String[] args) { double r = 4 , d = 3 ; shortdis(r, d); } } /* This code contributed by PrinciRaj1992 */ |
Python3
# Python program to find # the shortest distance from # chord to the centre of circle # Function to find the shortest distance def shortdis(r, d): print ( "The shortest distance " ,end = ""); print ( "from the chord to centre " ,end = ""); print (((r * r) - ((d * d) / 4 )) * * ( 1 / 2 )); # Driver code r = 4 ; d = 3 ; shortdis(r, d); # This code has been contributed by 29AjayKumar |
C#
// C# program to find // the shortest distance from // chord to the centre of circle using System; class GFG { // Function to find the shortest distance static void shortdis( double r, double d) { Console.WriteLine( "The shortest distance " + "from the chord to centre " + (Math.Sqrt((r * r) - ((d * d) / 4)))); } // Driver code public static void Main() { double r = 4, d = 3; shortdis(r, d); } } // This code is contributed by AnkitRai01 |
PHP
<?php // PHP program to find // the shortest distance from // chord to the centre of circle // Function to find the shortest distance function shortdis( $r , $d ) { echo "The shortest distance " ; echo "from the chord to centre " ; echo sqrt(( $r * $r ) - (( $d * $d ) / 4)); } // Driver code $r = 4; $d = 3; shortdis( $r , $d ); // This code is contributed by Naman_Garg. ?> |
Output:
The leshortest distance from the chord to centre 3.7081
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