2009
Problem - 3825
Each point of a circle is colored either red or blue.
(a) Prove that there always exists an isosceles triangle inscribed in this circle such that all its vertices are colored the same.
(b) Does there always exist an equilateral triangle inscribed in this circle such that all its vertices are colored the same?
(a) We can consider a regular pentagon. There must be three vertices be the same color. And It's an isosceles triangle
(b)It's false. We can draw the color like this: Half is red and the other is blue