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In a triangle $A B C, I$ is the incenter and $D, E, F$ the tangency points of the incircle with the sides $B C, C A, A B$, respectively. The line $A D$ intersects the incircle again at $P$. If $M$ is the midpoint of $E F$, prove that the points $P, I, M$ and $D$ lie on a circle.
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