### Brain Teasers

# Tangent Circles

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?

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

### Hint

It looks like a math teaser, but look at its category.### 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!Hide Hint Show Hint Hide Answer Show Answer

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## Comments

What??? I don't get this at all!

Don't worry me neither

I don't know much about circles.

This really should have gone in math

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.

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.

i am SO correcting this into math...

dduuuuuuuhhhhh.... wha?

Thanks for the explanation tsimkin, or I'd never have got this.

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.

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.

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.

tsimkin's explanation is a better one than the given answer, imo.

Yeah, this should have gone in math. There's no trick here.

Come on guys...... this ques has 2.05 difficulty. It is not worth of even 1.0 point.

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