Question 109
For an interior point $D$ of a triangle $ABC$, let $\Gamma_D$ denote the circle passing through the points $A$, $E$, $D$, $F$ if these points are concyclic where $BD \cap AC = \{E\}$ and $CD \cap AB = \{F\}$. Show that all circles $\Gamma_D$ pass through a second common point different from $A$ as $D$ varies.