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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 )
The diagonals of rhombus 5 and 10.
The area is 15.700000
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; }
The area of circle inscribed in the rhombus of diagonal 5 and 10 is 15.700000
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