2018 IMO Shortlist G3

A circle $\omega$ of radius 1 is given. A collection $T$ of triangles is called good, if the following conditions hold: (i) each triangle from $T$ is inscribed in $\omega$; (ii) 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 $t$. (South Africa)

给定一个半径为 1 的圆 $\omega$。如果满足以下条件，则三角形的集合 $T$ 被称为良好的： (i) $T$ 中的每个三角形都刻在 $\omega$ 中； (ii) $T$ 中没有两个三角形有公共内点。确定所有正实数 $t$，使得对于每个正整数 $n$，存在 $n$ 个三角形的良好集合，每个三角形的周长都大于 $t$。 (南非)