Brianchon's theorem has many important corollaries. For instance, in every pentagon circumscribed about a circle, the lines joining two pairs of nonadjacent vertices and the line through the fifth vertex and the point of tangency with its opposite side are concurrent. In every quadrilateral circumscribed about a circle, the two diagonals and the two lines joining points of tangency on opposite sides are concurrent. In every triangle circumscribed about a circle, the lines connecting the vertices with points of tangency of the opposite sides are concurrent. The dual of Brianchon's theorem is Pascal's theorem. Brianchon's theorem also applies to ellipses and more generally, to any conic section.