4 [ Angles subtended by equal arcs and equal chords]

On side $A B$ of rectangle $A B C D$, a point $M$ is chosen. Through this point, a perpendicular to line $C M$ is drawn, which intersects side $A D$ at point $E$. Point $P$ is the foot of the perpendicular dropped from point $M$ to line $C E$. Find the angle $A P B$.