IMO 2005 Problem 1
IMO 2005 Problem 1 is a plane geometry problem from the International Mathematical Olympiad 2005, Problem 1: an equilateral hexagon on the sides of an equilateral triangle.
Problem
Six points are chosen on the sides of an equilateral triangle $ABC$: $A_1$, $A_2$ on $BC$, $B_1$, $B_2$ on $CA$ and $C_1$, $C_2$ on $AB$, such that they are the vertices of a convex hexagon $A_1A_2B_1B_2C_1C_2$ with equal side lengths. Prove that the lines $A_1B_2$, $B_1C_2$ and $C_1A_2$ are concurrent.
Source International Mathematical Olympiad 2005, Problem 1
The diagram
Drag any point and the whole construction follows; ▶ runs a point along its segment and back. Tap a point to pin it, double-click to go back to the start. Effects redraws the figure in grayscale for print, in colour, or with the givens in focus.