What is the area of ​​a circle inscribed in a rhombus?

The inscribed circle of a rhombus is tangent to its four sides and four endpoints. The sides of the rhombus are tangent to the circle.

Here, r is the radius found using the diagonal of a and the given value.

Now the area triangle AOB = ½ * OA * OB = ½ * AB * r (both using the formula ½*b*h).

½ *a/2*b/2 = ½ *( √ (a2/4 b²/4))*r

a *b/8 = √ (a² b² )*r /4

r = a*b/ 2√ (a² b² )

Circle area = π*r*r = π*(a²*b²)/4(a² support> b² )

Example

The diagonals of rhombus 5 and 10.

The area is 15.700000

Sample code

Real-time demonstration

#include <stdio.h>
int main(void) {
   int a = 5; int b= 10;
   float pie = 3.14;
   float area = (float)((pie*a*a*b*b)/(4*((a*a)+(b*b))));
   printf("The area of circle inscribed in the rhombus of diagonal %d and %d is %f",a,b,area);
   return 0;
}

Output

The area of circle inscribed in the rhombus of diagonal 5 and 10 is 15.700000

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