CN-LEAGUE 2021 Problem 2

In $\triangle ABC$ , point $M$ is the middle point of $AC$ . $MD//AB$ and meet the tangent of $A$ to $\odot(ABC)$ at point $D$ . Point $E$ is in $AD$ and point $A$ is the middle point of $DE$ . $\{P\}=\odot(ABE)\cap AC,\{Q\}=\odot(ADP)\cap DM$ . Prove that $\angle QCB=\angle BAC$ .