A degenerate case of Pascal's theorem (four points) is interesting; given points on a conic , the intersection of alternate sides, , , together with the intersection of tangents at opposite vertices and are collinear in four points; the tangents being degenerate 'sides', taken at two possible positions on the 'hexagon' and the corresponding Pascal line sharing either degenerate intersection. This can be proven independently using a property of pole-polar. If the conic is a circle, then another degenerate case says that for a triangle, the three points that appear as the intersection of a side line with the corresponding side line of the Gergonne triangle, are collinear.