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

**Theorem:** *Take three conics. Suppose that each of them touch a 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