Every point on a circle is coloured in blue or yellow
Source: Moldova JTST 2023
May 5, 2023
combinatorics
Problem Statement
Every point on a circle is coloured in blue or yellow such there is at least a point of each color.
Prove that for every colouring of the circle there is always an isosceles triangle inscribed inside the circle
1) with all vertexes of the same colour.
2) with vertexes of both colours.
For every colouring of the circle is there an equilateral triangle inscribed inside the circle
3) with all vertexes of the same colour?
4) with vertexes of both colours?