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.

Rauhan Jan 12, 2017

#1**+5 **

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

CPhill Jan 13, 2017