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In front of me stands a table with the shape of an equilateral triangle with side lengths 1.

I can cover the whole surface with five identical circular tablecloths.

What is the minimum radius for a tablecloth? (The tablecloths can of course overlap).

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Here's a covering with tablecloths of radius $1/4$:

enter image description here

It's not possible to use tablecloths of a smaller radius, because you cannot reach all of the six points marked in red with only five tablecloths.

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