What is the area of ​​a circle within a rectangle inscribed in a semicircle?

A circle inscribed in a rectangle is tangent to the longer side of the rectangle, that is, the length is tangent to the circle.

A rectangle inscribed in a semicircle touches two points on the arc of the semicircle. The width of the rectangle is equal to the diameter of the circle.

If R is the radius of the semicircle.

The length of the rectangle = √2R/2

The width of the rectangle = R/√2

Inscribed circle The radius of is

r = b/2 = R/2√2

Using this formula we can calculate The area of ​​a circle inscribed in a rectangle inscribed in a semicircle,

area = (π*r²) = π*R/8

Example

Demonstration

#include <stdio.h>
int main() {
   float a = 5;
   float area = 3.14 * a/ 8;
   printf("The area of the circle inscribed in a rectangle inscribed in a semicircle of radius %f is %f", a , area);
   return 0;
}

Output

The area of the circle inscribed in a rectangle inscribed in a semicircle of radius 5.00000 is 1.962500

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