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