+502 The large circle has a radius of 10 cm. Find the radius of the largest circle which will fit in the middle.
The picture is something like this.
+128403 We have this :
Let AB = 2r cm where r is the radius of each small circle
And DB = √2 *2r cm
And we have that 2r + √2 *2r = 20 → r + √2r = 10 → r = 10 / [ 1 + √2] cm
So the radius of the small circle in the center = √2r − r =
[ 10√2] * / [ 1 + √2] ] − 10 / [ 1 + √2] cm =
[10 ( √2− 1) ] / [ 1 + √2] cm ≈
[1.71572875....] cm
