I found a remarkable theorem of four conics as follows [some year ago](http://oaithanhdao.blogspot.com/2014/10/80-another-four-conics-theorem.html). But has no proof, I am looking for a proof:

**Theorem:** *Let three conics and one of them touch with fourth conic at two points. Then remaining pair of common tangents intersect at three collinear points.*

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/gyhnu.png