Question

the large circle has a radius of 10 cm.find the radius of the largest circle which will fit in the middle

Answer 1

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