Let $ABC$ be a triangle and $K$ be its circumcircle. Let $P$ be the point of intersection of $BC$ with tangent in $A$ to $K$. Let $D$ and $E$ be the symmetrical points of $B$ and $A$, respectively, from $P$. Let $K_1$ be the circumcircle of triangle $DAC$ and let $K_2$ the circumscribed circle of triangle $APB$. We denote with $F$ the second intersection point of the circles $K_1$ and $K_2$ Then denote with $G$ the second intersection point of the circle $K_1$ with $BF$. Show that the lines $BC$ and $EG$ are parallel.