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Geometric game: Maximizing area

Source: Germany 2016 - BWM Round 1, #2

November 12, 2016
geometrygeometry unsolvedarea of a triangleareaGame Theory

Problem Statement

A triangle ABCABC with area 11 is given. Anja and Bernd are playing the following game: Anja chooses a point XX on side BCBC. Then Bernd chooses a point YY on side CACA und at last Anja chooses a point ZZ on side ABAB. Also, X,YX,Y and ZZ cannot be a vertex of triangle ABCABC. Anja wants to maximize the area of triangle XYZXYZ and Bernd wants to minimize that area. What is the area of triangle XYZXYZ at the end of the game, if both play optimally?
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