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# Area of circle inscribed within rhombus?

Circle inscribed in a rhombus touches its four side a four ends. The side of rhombus is a tangent to the circle.

Here, r is the radius that is to be found using a and, the diagonals whose values are given.

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

½ *a/2*b/2 = ½ *( √ (a^{2}/4 + b^{2}/4))*r

a*b/8 = √ (a^{2}+ b^{2} )*r /4

r = a*b/ 2√ (a^{2}+ b^{2} )

Area of circle = π*r*r = π*(a^{2}*b^{2})/4(a^{2}+ b^{2} )

## Example

The diagonal of the rhombus 5 & 10.

Area is 15.700000

## Example Code

#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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