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 circle float 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 code int main()
{ float R = 2;
cout << circlearea(R) << endl;
return 0;
} |
Java
// Java Program to find the biggest circle // which can be inscribed within the semicircle 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 ;
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 circle def 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 code if __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 semicircle using 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 circle function 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 code var 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)