Tangent Circles
Trick brain teasers appear difficult at first, but they have a trick that makes them really easy.
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?
HintIt looks like a math teaser, but look at its category.
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Answer
The four circles can be tangent to each other at the same point, therefore there is no upper bound to the radius of the fourth circle!
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Comments
Marple
Jan 11, 2012
 What??? I don't get this at all! 
babyjuice
Jan 12, 2012
 Don't worry me neither 
YJunjie
Jan 24, 2012
 I don't know much about circles. 
tuffysos0915
Apr 14, 2012
 This really should have gone in math 
tsimkin
Apr 18, 2012
 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. 
dangerouspie101
May 09, 2012
 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. 
dangerouspie101
Jun 16, 2012
 i am SO correcting this into math... 
Candi7
Jun 20, 2012
 dduuuuuuuhhhhh.... wha? 
JQPublic
Aug 05, 2012
 Thanks for the explanation tsimkin, or I'd never have got this. 
spikethru4
Dec 03, 2012
 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 lopsided 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. 
spikethru4
Dec 04, 2012
 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. 
TheRiddleTroll
Dec 11, 2016
 Yeah, this should have gone in math. There's no trick here. 
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