How to prove parallel line of internally tangent circles?

Question

Let P be the point where 2 circles tangent internally and $PA$, $PB$ intersect the small circle at $E$ and $F$ respectively where $A$ and $B$ is on the big circle. So how could we prove that $EF$ is parallel to $AB$? I'm having problem proving this and I don't know if there is any theorem about it. Please help

Answer 1

First prove it for the case that one of $PA$ or $PB$ goes through the centers. Then prove it for two other cases that centers place between them or outside.