Radius of the circle when the width and height of an arc is given - GeeksforGeeks

19 Apr, 2021
Given a circle in which the width and height of an arc are given. The task is to find the radius of the circle with the help of the width and height of the arc.Examples:  
Input: d = 4, h = 1 
Output: The radius of the circle is 2.5

Input: d = 14, h = 8
Output: The radius of the circle is 7.0625
 
Approach  
Let the radius of the circle be r
Let the height and width of the arc be h & d
Now, the diameter DC bisects the chord AB in two halves, each having length d/2
Also the diameter is divided by the chord in two parts, the part inside arc h and the remaining 2r-h
Now from intersecting chords theorem, h*(2r-h) = (d/2)^2 or, 2rh – h^2 = d^2/4 so, r = d^2/8h + h/2
So, radius of the circle 
C++
Java
Python3
C#
PHP
Javascript
// C++ program to find// radius of the circle// when the width and height// of an arc is given #include <bits/stdc++.h>using namespace std; // Function to find the radiusvoid rad(double d, double h){    cout << "The radius of the circle is "        << ((d * d) / (8 * h) + h / 2)        << endl;} // Driver codeint main(){    double d = 4, h = 1;    rad(d, h);    return 0;}
// Java program to find// radius of the circle// when the width and height// of an arc is givenclass GFG{ // Function to find the radiusstatic void rad(double d, double h){    System.out.println( "The radius of the circle is "        + ((d * d) / (8 * h) + h / 2));} // Driver codepublic static void main(String[] args){    double d = 4, h = 1;    rad(d, h);}} /* This code contributed by PrinciRaj1992 */
# Python3 program to find# radius of the circle# when the width and height# of an arc is given # Function to find the radiusdef rad(d, h):    print("The radius of the circle is",        ((d * d) / (8 * h) + h / 2)) # Driver coded = 4; h = 1;rad(d, h); # This code is contributed by 29AjayKumar
// C# program to find// radius of the circle// when the width and height// of an arc is givenusing System; class GFG{ // Function to find the radiusstatic void rad(double d, double h){    Console.WriteLine( "The radius of the circle is "        + ((d * d) / (8 * h) + h / 2));} // Driver codepublic static void Main(){    double d = 4, h = 1;    rad(d, h);}} // This code is contributed by AnkitRai01
<?php// PHP program to find radius of// the circle when the width and// height of an arc is given // Function to find the radiusfunction rad($d, $h){    echo "The radius of the circle is ",        (($d * $d) / (8 * $h) + $h / 2), "\n";} // Driver code$d = 4;$h = 1;rad($d, $h); // This code is contributed by ajit?>
<script> // Javascript program to find// radius of the circle// when the width and height// of an arc is given // Function to find the radiusfunction rad(d, h){    document.write("The radius of the circle is "    +((d * d) / (8 * h) + h / 2));} // Driver code    var d = 4, h = 1;    rad(d, h); </script>
Output:
The radius of the circle is 2.5
princiraj1992
ankthon
29AjayKumar
jit_t
bgangwar59
Geometric
Mathematical
Mathematical
Geometric
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