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Tangent Circles

Category:Trick
Submitted By:shenqiang
Fun:** (1.65)
Difficulty:** (2.02)



Four circles are situated in the plane so that each is tangent to the other three.

If three of the radii are 3, 4, and 5, what's the largest possible radius of the fourth circle?

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Comments on this teaser


Posted by Marple01/11/12
What??? I don't get this at all! :o :o :oops:

Posted by babyjuice01/12/12
Don't worry me neither

Posted by YJunjie01/24/12
I don't know much about circles. :-?

Posted by tuffysos091504/14/12
This really should have gone in math

Posted by tsimkin04/18/12
Of course the can all be tangent. Imagine that the smaller circles are inside of the larger ones. They can be tangent at the same point on their perimeter. The largest circle that could also be tangent would have an infinitely large radius.

Posted by dangerouspie10105/09/12
What the heck? It made NOOOO sense what so ever to me. It should of gone in math because you arent supossed to need more that basic math skills to solve these. I had no idea what was be said, and Im in advanced math.

Posted by dangerouspie10106/16/12
i am SO correcting this into math...

Posted by Candi706/20/12
dduuuuuuuhhhhh.... wha? :-?

Posted by JQPublic08/05/12
Thanks for the explanation tsimkin, or I'd never have got this. :D

Posted by spikethru412/03/12
The teaser doesn't specify that the circles are all tangent at the same point. Take the three smaller circles and arrange them so that they are touching each other externally - kind of like a Mickey Mouse silhouette with lop-sided ears! Then a fourth circle can be described around the outer edges of the other three, which will be tangent to all of them. The radius of this circle is a little over 9.

Posted by spikethru412/04/12
OK, retract that comment. I've just read the question and answer again properly (saw 'can't be tangent at the same point' before) and it all makes sense now. tsimkin's explanation is a better one than the given answer, imo.




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