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6

Part of 2014 Lusophon Mathematical Olympiad

Problems(1)

IV Lusophon Mathematical Olympiad 2014 - Problem 6

Source:

12/29/2014
Kilua and Ndoti play the following game in a square ABCDABCD: Kilua chooses one of the sides of the square and draws a point XX at this side. Ndoti chooses one of the other three sides and draws a point Y. Kilua chooses another side that hasn't been chosen and draws a point Z. Finally, Ndoti chooses the last side that hasn't been chosen yet and draws a point W. Each one of the players can draw his point at a vertex of ABCDABCD, but they have to choose the side of the square that is going to be used to do that. For example, if Kilua chooses ABAB, he can draws XX at the point BB and it doesn't impede Ndoti of choosing BCBC. A vertex cannot de chosen twice. Kilua wins if the area of the convex quadrilateral formed by XX, YY, ZZ, and WW is greater or equal than a half of the area of ABCDABCD. Otherwise, Ndoti wins. Which player has a winning strategy? How can he play?
geometry