four small circle of radius 1 are tangent to each other and to a large circle containing them what is - Maths - Circles

Question

​four small circle of radius 1 are tangent to each other and
to a large circle containing them what is the area of the region
inside the larger circle but outside all the smaller circle

Brijendra Pal · Accepted Answer

Dear STudent, Look at just one quadrant

As you can see from the diagram, the green line along with the two radii form a square of side,

The distance from the origin to the larger circle (the radius of the larger circle) is equal to the diagonal of the square (blue line) plus the radius of the small circle D=sqrt%282%29%2AR

Since R=1, then, Rbig=1%281%2Bsqrt%282%29%29

Now Required area = πRbig2-4πR2=π2+12-4×1= π22-1 cm2Regards

​four small circle of radius 1 are tangent to each other and to a large circle containing them what is the area of the region inside the larger circle but outside all the smaller circle

four small circle of radius 1 are tangent to each other and to a large circle containing them what is the area of the region inside the larger circle but outside all the smaller circle