Let P be a convex 1986-gon in the plane. Let A,D be interior points of two distinct sides of P and let B,C be two distinct interior points of the line segment AD. Starting with an arbitrary point Q1 on the boundary of P, define recursively a sequence of points Qn as follows:
given Qn extend the directed line segment QnB to meet the boundary of P in a point Rn and then extend RnC to meet the boundary of P again in a point, which is defined to be Qn+1. Prove that for all n large enough the points Qn are on one of the sides of P containing A or D. geometry unsolvedgeometry