Covering a circle

Geometry Level 1

Circles have the strange property that if you increase the size of any circle by even the tiniest amount, you need at least three circles of the original size in order to completely cover the new, slightly larger circle.

Are there any other shapes that share this property?

The 3 overlapping orange circles have the same radius as the black circle.  It takes 3 of these circles to cover the slightly larger dashed circle. The 3 overlapping orange circles have the same radius as the black circle. It takes 3 of these circles to cover the slightly larger dashed circle.


Note 1: For other shapes, rather than increasing their radius, which is generally only associated with circles, you are scaling up their shape proportionally.

Note 2: You can rotate the shapes any way you like.

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