circles cover triangle

Question

Please help to solve this question:

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

Thanks

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. — Calvin Lin, Jan 12 '13 at 16:32
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? — Calvin Lin, Jan 12 '13 at 16:53

score 4 · Answer 1 · answered Jan 13 '13 at 09:27

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).

1 Answers1