Question 10
In the plane a circle $\omega$ of radius $1$ is given. A set $T$ of triangles is called good if it satisfies the following two conditions:
(i) every triangle in $T$ is inscribed in $\omega$,
(ii) no two triangles in $T$ have a common interior point.
Determine all positive real numbers $t$ such that, for every positive integer $n$, there exists a good set $T$ consisting of $n$ triangles, each of which has perimeter greater than $t$.
(i) every triangle in $T$ is inscribed in $\omega$,
(ii) no two triangles in $T$ have a common interior point.
Determine all positive real numbers $t$ such that, for every positive integer $n$, there exists a good set $T$ consisting of $n$ triangles, each of which has perimeter greater than $t$.