The study of geometric objects defined by polynomial equations, as well as their generalizations: algebraic curves, such as elliptic curves, and more generally algebraic varieties, schemes, etc. Problems under this tag typically involve techniques of abstract algebra or complex-analytic methods. ...

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The intersection points are collinear

It is given a hexagon inscribed in a conic section. I want to prove that the pairs of opposite site intersect at three points of the projective plane that are collinear. How could we do this? ...