cirkels door 2 punten geteld met multipliteit

Let $C_1,C_2$ be circles intersecting in $X,Y$. Let $A,D$ be points on $C_1$ and $B,C$ on $C_2$ such that $A,X,C$ are collinear and $D,X,B$ are collinear. The tangent to circle $C_1$ at $D$ intersects $BC$ and the tangent to $C_2$ at $B$ in $P,R$ respectively. The tangent to $C_2$ at $C$ intersects $AD$ and tangent to $C_1$ at $A$, in $Q,S$ respectively. Let $W$ be the intersection of $AD$ with the tangent to $C_2$ at $B$ and $Z$ the intersection of $BC$ with the tangent to $C_1$ at $A$. Prove that the circumcircles of triangles $YWZ,RSY$ and $PQY$ have two points in common, or are tangent in the same point.