Pascal's theorem

Pascal's theorem is a result about a special shape called a hexagon (a six-sided polygon) that is drawn inside a circle. The theorem says: If you draw any hexagon inside a circle (the vertices can be anywhere on the circle), and then extend its opposite sides so they meet, the three points where these pairs of sides meet will always lie on a straight line.

Important properties

• Works for any hexagon inscribed in a circle, even if the hexagon crosses itself.

• The line on which the intersection points lie is called the Pascal line.

• The theorem is a generalization of the property that the opposite sides of a cyclic quadrilateral meet at collinear points (degenerate case).