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The points Qn are on one of the sides of P containing A or D

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August 29, 2010
geometry unsolvedgeometry

Problem Statement

Let PP be a convex 19861986-gon in the plane. Let A,DA,D be interior points of two distinct sides of P and let B,CB,C be two distinct interior points of the line segment ADAD. Starting with an arbitrary point Q1Q_1 on the boundary of PP, define recursively a sequence of points QnQ_n as follows: given QnQ_n extend the directed line segment QnBQ_nB to meet the boundary of PP in a point RnR_n and then extend RnCR_nC to meet the boundary of PP again in a point, which is defined to be Qn+1Q_{n+1}. Prove that for all nn large enough the points QnQ_n are on one of the sides of PP containing AA or DD.
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