Question 17
(CHN 3) IMO2. Let $A,B,C$ be fixed points in the plane. A man starts from a certain point $P_0$ and walks directly to $A$. At $A$ he turns his direction by $60^\circ$ to the left and walks to $P_1$ such that $P_0A=AP_1$. After he does the same action 1986 times successively around the points $A,B,C,A,B,C,\ldots$, he returns to the starting point. Prove that $\triangle ABC$ is equilateral and that the vertices $A,B,C$ are arranged counterclockwise.