First Geometry in 2019

A circle $\omega$ of radius $1$ is given. A collection $T$ of triangles is called good, if the following conditions hold:

1. Each triangle from $T$ is inscribed in $\omega$ ;
2. No two triangles from $T$ have a common interior point.

Let the positive real number $t$ be such that, for each positive integer $n$ , there exists a good collection of $n$ triangles, each of perimeter greater than $t$ . Find the upper bound of $t$ .