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.
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!
Jan 11, 2012
|What??? I don't get this at all! |
Jan 12, 2012
|Don't worry me neither|
Jan 24, 2012
|I don't know much about circles. |
Apr 14, 2012
|This really should have gone in math|
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.|
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.|
Jun 16, 2012
|i am SO correcting this into math...|
Jun 20, 2012
|dduuuuuuuhhhhh.... wha? |
Aug 05, 2012
|Thanks for the explanation tsimkin, or I'd never have got this. |
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.
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.
Dec 11, 2016
|Yeah, this should have gone in math. There's no trick here.|
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