Three circles of radius \(s\) are drawn in the first quadrant of the \(xy\)-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the \(x\)-axis, and the third is tangent to the first circle and the \(y\)-axis. A circle of radius \(r>s\) is tangent to both axes and to the second and third circles. What is \(r/s\)?

Guest Dec 26, 2018

#1**0 **

3 / (sqrt 2 - 1) ? Anyone else?

3 sqrt2 / (sqrt2-1) ?

8 ? Now I'm just guessing! I have no idea!

ElectricPavlov Dec 26, 2018

edited by
ElectricPavlov
Dec 26, 2018

edited by ElectricPavlov Dec 26, 2018

edited by ElectricPavlov Dec 26, 2018

edited by ElectricPavlov Dec 26, 2018

edited by ElectricPavlov Dec 26, 2018

#2**+3 **

The answer is approximately 9 (maybe exactly 9)

But I have not worked out how to do it properly.

Melody Dec 27, 2018

#5

#7**+1 **

Sorry Alan, it has just been pointed out to me that it was your post.

Thanks for your clear explanation :)

Melody
Dec 27, 2018

#8**+2 **

Thanx, Alan..... I looked at that one for some time, but could not find an answer ! You made it look too easy.....

ElectricPavlov
Dec 27, 2018