geometry problems from Lotfi Zadeh Olympiad from Azerbaijan, with aops links in the names
collected inside aops here
In the inscribed quadrilateral $ABCD$, $P$ is the intersection point of diagonals and $M$ is the midpoint of arc $AB$. Prove that line $MP$ passes through the midpoint of segment $CD$, if and only if lines $AB, CD$ are parallel.
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