Question 67
Let $\Gamma$ be the incircle of square $ABCD$. Let $M$ be the midpoint of segment $CD$, and let $P$ be a point on segment $AB$ different from $B$. Let $E$ be a point on $\Gamma$ different from $M$ such that the line $DP$ is parallel to the line $EM$. Let the lines $CP$ and $AD$ meet at $F$. Prove that the line $EF$ is tangent to $\Gamma$.