Problem #PRU-35758

Problems Geometry Plane geometry Triangles Incirlce and circumcircle of a triangle Polygons Pentagons Methods Pigeonhole principle Pigeonhole principle (finite number of poits, lines etc.) Regular polygons
 13–14  3.0

Problem

All the points on the edge of a circle are coloured in two different colours at random. Prove that there will be an equilateral triangle with vertices of the same colour inside the circle – the vertices are points on the circumference of the circle.