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# Area of a circle inscribed in a rectangle which is inscribed in a semicircle in C?

A circle inscribed in a rectangle touches the larger side of the rectangle with its ends i.e. the length is tangent to the circle.

A rectangle inscribed in a semicircle touches its arc at two points. The breadth of the rectangle is equal to the diameter of the circle.

If **R** is the radius of semi-circle.

Length of the rectangle = √2**R**/2

Breadth of the rectangle = **R**/√2

Radius of biggest circle inscribed is

**r** = **b**/2 = **R**/2√2

Using this formula we can find the area of this circle inscribed in a rectangle which is inscribed in a semicircle,

**Area = (π*r ^{2}) = π*R/8**

## Example

#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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