Circling The Square Puzzle - Solution

The Puzzle:

Circling The Square
In the diagram below, each circle is just big enough to touch all four sides of the square. The area of the square is therefore just a bit more than the area of one of the circles.



I want to know how many of the circles you need to cover the whole square. Is 2 enough? Or do you need 3? Or 4? Or more?

I have put 5 circles for you to play with (print and then cut them out), but what is the least number you need?




Our Solution:

The actual answer is that you need FOUR circles to cover the square completely.



But because it is so difficult to cut out the circles accurately enough to see the tiny gaps that appear, you can be happy if you answered three circles. But four is correct, and you can actually use a program like "GeoGebra" to solve it.



Puzzle Author: Stephen Froggatt

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