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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 \(r/s\)

 Dec 26, 2018
 #1
avatar+17332 
0

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

 

3 sqrt2 / (sqrt2-1)  ?

 

 

 

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

 Dec 26, 2018
edited by ElectricPavlov  Dec 26, 2018
edited by ElectricPavlov  Dec 26, 2018
edited by ElectricPavlov  Dec 26, 2018
 #2
avatar+99331 
+3

The answer is approximately 9 (maybe exactly 9)

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

 

 Dec 27, 2018
 #3
avatar+4459 
0

9 is the correct answer.

 

I don't know how to derive it.  It can be verified w/o too much trouble.

Rom  Dec 27, 2018
 #4
avatar+99331 
0

Thanks Rom, How do you verify it?

Melody  Dec 27, 2018
 #5
avatar+27547 
+3

As follows:

 

 Dec 27, 2018
 #6
avatar+99331 
+1

Thanks Rom, that makes perfect sense.

Melody  Dec 27, 2018
 #7
avatar+99331 
+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
avatar+17332 
+2

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

ElectricPavlov  Dec 27, 2018
 #9
avatar+27547 
+2

The trick is to find the right way to look at the problem. It took me a while to find the right way!

Alan  Dec 27, 2018
 #10
avatar+98172 
+1

Very nice, alan.....!!

 

Sometimes, over-complicating things is the worst approach....

 

 

cool cool cool

CPhill  Dec 27, 2018
 #11
avatar+99331 
+2

It was a great problem.

It had a few of us in a head spin!  

Thanks again for your great solution Alan :)

 Dec 27, 2018

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