Given a semicircle with radius R, the task is to find the area of the largest circle that can be inscribed in the semicircle.
Examples:
Input: R = 2 Output: 3.14 Input: R = 8 Output: 50.24
Approach: Let R be the radius of the semicircle
- For Largest circle that can be inscribed in this semicircle, the diameter of the circle must be equal to the radius of the semi-circle.
- So, if the radius of the semi-circle is R, then the diameter of the largest inscribed circle will be R.
- Hence the radius of the inscribed circle must be R/2
- Therefore the area of the largest circle will be
Area of circle = pi*Radius2
= pi*(R/2)2
since the radius of largest circle is R/2
where R is the radius of the semicircle
Below is the implementation of the above approach:
C++
// C++ Program to find the biggest circle// which can be inscribed within the semicircle#include <bits/stdc++.h>using namespace std;// Function to find the area// of the circlefloat circlearea(float R){ // Radius cannot be negative if (R < 0) return -1; // Area of the largest circle float a = 3.14 * R * R / 4; return a;}// Driver codeint main(){ float R = 2; cout << circlearea(R) << endl; return 0;} |
Java
// Java Program to find the biggest circle// which can be inscribed within the semicircleclass GFG { // Function to find the area // of the circle static float circlearea(float R) { // Radius cannot be negative if (R < 0) return -1; // Area of the largest circle float a = (float)((3.14 * R * R) / 4); return a; } // Driver code public static void main (String[] args) { float R = 2; System.out.println(circlearea(R)); }}// This code is contributed by AnkitRai01 |
Python3
# Python3 Program to find the biggest circle# which can be inscribed within the semicircle# Function to find the area# of the circledef circlearea(R) : # Radius cannot be negative if (R < 0) : return -1; # Area of the largest circle a = (3.14 * R * R) / 4; return a;# Driver codeif __name__ == "__main__" : R = 2; print(circlearea(R)) ; # This code is contributed by AnkitRai01 |
C#
// C# Program to find the biggest circle// which can be inscribed within the semicircleusing System;class GFG { // Function to find the area // of the circle static float circlearea(float R) { // Radius cannot be negative if (R < 0) return -1; // Area of the largest circle float a = (float)((3.14 * R * R) / 4); return a; } // Driver code public static void Main (string[] args) { float R = 2; Console.WriteLine(circlearea(R)); }}// This code is contributed by AnkitRai01 |
Javascript
<script>// Javascript Program to find the biggest circle// which can be inscribed within the semicircle// Function to find the area// of the circlefunction circlearea(R){ // Radius cannot be negative if (R < 0) return -1; // Area of the largest circle var a = 3.14 * R * R / 4; return a;}// Driver codevar R = 2;document.write(circlearea(R));// This code is contributed by rutvik_56.</script> |
Output:
3.14
Time Complexity: O(1)
Auxiliary Space: O(1)
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