A middle

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Let $PA$ are $PB$ the tangents from point $P$ to a circle $k$. A line parallel to $PA$ intersects $AB$ and $k$ at the points $C$ and $D$ respectively. $PD$ intersects $k$ at the point $E$. $M$ is the intersection point of $PA$ and $CE$. Prove that $M$ is the middle of $PA$.

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Maybe I double posted the problem. It can be solved using the following result: topic43754.html