Circle, diameter and parallel lines

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Let $PA$ is a tangent to the circle $k$. A line through $P$ intersects $k$ at the points $B$ and $C$. Through $C$ is drawn line, parallel to $PA$ that intersects $k$ at the point $D$. The diameter through $D$ intersects $AB$ and $k$ at the points $E$ and $F$ respectively. If $Q$ is the intersection point of $AF$ and $PB$. Prove that $EQ || AP$.