Brianchon's theorem

Brianchon's theorem is a result in projective geometry concerning hexagons and conics. It states that if a hexagon is inscribed in a conic section (like an ellipse, parabola, or hyperbola) and the opposite sides of the hexagon are extended to meet, then the three intersection points of these extended lines will be collinear. More formally, consider a hexagon \( ABCDEF \) inscribed in a conic.