Given a circle $\omega$ with radius $1$. Let $T$ be a set of triangles good, if the following conditions apply: (a) the circumcircle of each triangle in the set $T$ is $\omega$; (b) The interior of any two triangles in the set $T$ has no common point. Find all positive real numbers $t$, for which for each positive integer $n$ there is a good set of $n$ triangles, where the perimeter of each triangle is greater than $t$.
Problem
Source: Estonia IMO TST 2019 p11
Tags: circumcircle, combinatorial geometry, perimeter, geometry
25.04.2021 02:25
Is it correct the statement?
25.04.2021 09:48
parmenides51 wrote: Given a circle $\omega$ of radius $1$. We call a set of triangles $T$ good if the following conditions are satisfied: a) for each triangle from the set $T$, the circle $\omega$ is circumscribed, b) the interior regions of no two triangles of the set $T$ have common points. Find all positive real numbers $t$ for which for for every positive integer $n$, there is a good collection of $n$ triangles, the perimeter of each of which is greater than $t$ just updated to wording to Quote: Given a circle $\omega$ with radius $1$. Let $T$ be a set of triangles good, if the following conditions apply: (a) the circumcircle of each triangle in the set $T$ is $\omega$; (b) The interior of any two triangles in the set $T$ has no common point. Find all positive real numbers $t$, for which for each positive integer $n$ there is a good set of $n$ triangles, where the perimeter of each triangle is greater than $t$.
10.01.2023 15:25