The first example shows Pascals' Theorem: If (A,B,C,D,E,G) are six points on a conic, then the intersections of lines AC and BE,AD and BG, and CG and DE are kollinear.

The second drawing shows the projective dual Theorem of Brianchon - just interchange "point" with "line", "intersection" with "connecting line" and "on conic" with "tangent to conic".

For better identification the lines corresponding to points in the first figure have the same color coding.

This is an interactive applet created with Cinderella, you can drag the points in the first figure, and both Pascals' and Brianchons' theorem will be updated accordingly.