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ASU 206 All Soviet Union MO 1975 triangle area game strategy

Source:

July 5, 2019
geometrygame strategyareas

Problem Statement

Given a triangle ABCABC with the unit area. The first player chooses a point XX on the side [AB][AB], than the second -- YY on [BC][BC] side, and, finally, the first chooses a point ZZ on [AC][AC] side. The first tries to obtain the greatest possible area of the XYZXYZ triangle, the second -- the smallest. What area can obtain the first for sure and how?
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