### 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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