Cayley-bacharach theorem proof

          Pole and polar of a circle pdf.

          Pappus and desargues

          Brianchon's theorem

          The 3 long diagonals of a hexagon tangent to a conic section meet in a single point

          In geometry, Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal diagonals (those connecting opposite vertices) meet in a single point.

          It is named after Charles Julien Brianchon (1783–1864).

          Formal statement

          Let be a hexagon formed by six tangent lines of a conic section. Then lines (extended diagonals each connecting opposite vertices) intersect at a single point, the Brianchon point.[1]: p.

          Charles julien brianchon

        1. Brokard theorem
        2. Pole and polar of a circle pdf
        3. Define pole and polar
        4. Classification of conics

          5. 218 [2]

          Connection to Pascal's theorem

          The polar reciprocal and projective dual of this theorem give Pascal's theorem.

          Degenerations

          As for Pascal's theorem there exist degenerations for Brianchon's theorem, too: Let coincide two neighbored tangents.

          Their point of intersection becomes a point of the conic. In the diagram three pairs of neighbored tangents coincid