MathDB

A circle

\omega

with radius

1

is given. A collection

T

of triangles is called good, if the following conditions hold:
[*] each triangle from

T

is inscribed in

\omega

; [*] no two triangles from

T

have a common interior point.
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

Problem Statement