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Omni-MATH / A circle ω with radius 1 is given. A collection T of triangles is called [i]good[/i], if the following conditions hold: [list=1] [*] each triangle from T is inscribed in ω; [*] no …

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problem

A circle ω\omega with radius 11 is given. A collection TT of triangles is called [i]good[/i], if the following conditions hold: [list=1] [*] each triangle from TT is inscribed in ω\omega; [*] no two triangles from TT have a common interior point. [/list] Determine all positive real numbers tt such that, for each positive integer nn, there exists a good collection of nn triangles, each of perimeter greater than tt.
Plain-text mathematical notation (without MathML)
A circle ω with radius 1 is given. A collection T of triangles is called [i]good[/i], if the following conditions hold:
[list=1]
[*] each triangle from T is inscribed in ω;
[*] no two triangles from T have a common interior point.
[/list]
Determine all positive real numbers t such that, for each positive integer n, there exists a good collection of n triangles, each of perimeter greater than t.
Original LaTeX notation
A circle $\omega$ with radius $1$ is given. A collection $T$ of triangles is called [i]good[/i], if the following conditions hold:
[list=1]
[*] each triangle from $T$ is inscribed in $\omega$;
[*] no two triangles from $T$ have a common interior point.
[/list]
Determine all positive real numbers $t$ such that, for each positive integer $n$, there exists a good collection of $n$ triangles, each of perimeter greater than $t$.

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task_id
18620af7-899b-59ac-aea0-75e5d15bda33
task_key
test--18620af7-899b-59ac-aea0-75e5d15bda33
task_revision_id
1
config / split
/ test

Official source

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