PIXIE and VEDANSI play a triangle game. PIXIE fi rst draws a triangle ABC with area 1, and
VEDANSI picks a point X inside the triangle ABC. pixie then draws segments DG, EH, and FI,
all through X, such that D and E are on BC, F and G are on AC, and H and I are on AB. The ten
points must all be distinct. Finally, let S be the sum of the areas of triangles DEX, FGX, and HIX. VEDANSI earns S points, and PIXIE earns (1 - S) points. If both players play optimally to maximize
the amount of points they get, who will win and by how much?
VEDANSI picks a point X inside the triangle ABC. pixie then draws segments DG, EH, and FI,
all through X, such that D and E are on BC, F and G are on AC, and H and I are on AB. The ten
points must all be distinct. Finally, let S be the sum of the areas of triangles DEX, FGX, and HIX. VEDANSI earns S points, and PIXIE earns (1 - S) points. If both players play optimally to maximize
the amount of points they get, who will win and by how much?
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