Please help to solve this question:

three circles cover triangle. Can they still cover any triangle with decreased sides ?


  • 3
    $\begingroup$ You need to be more descriptive. How do they cover the triangle? I can place 3 huge circles that each cover the triangle. Yes, they will still cover with decreased sides. $\endgroup$ – Calvin Lin Jan 12 '13 at 16:32
  • $\begingroup$ Do you have a diagram of what you're taking about? Do the 3 circles have a common point? Does every 2 circles have another common point on the side of the triangle? Does every circle pass through a vertex of the triangle? $\endgroup$ – Calvin Lin Jan 12 '13 at 16:53

Consider a triangle with side lengths (1, 1, 1.99999) it is very nearly a straight line and can be covered using 3 circles of radius 1/3.

Assuming that we are not allowed to move them, the same three circles would not cover the triangle with side lengths (1, 1, 1).


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