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## Tangent Circles

Trick brain teasers appear difficult at first, but they have a trick that makes them really easy.

 Puzzle ID: #49219 Fun: (1.65) Difficulty: (2.02) Category: Trick Submitted By: shenqiang

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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 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 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. 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.