Question 94
Let $ABCDEF$ be a cyclic and convex hexagon. A point $P$ is called *admissible* if it does not lie on the circumcircle of $ABCDEF$ or on any of the lines $AD$, $BE$ and $CF$. An admissible point is called *fantastic* if $\odot(ADP)$, $\odot(BEP)$ and $\odot(CFP)$ intersect in exactly two points. Prove that if there exists a fantastic point, then all admissible points are fantastic.