72. Consider the quadrilateral $D E P M, \angle D E M=\angle D P M=90^{\circ}$, therefore, this quadrilateral is cyclic. Hence, $\angle D M E=$ $=\angle D P E=45^{\circ}$. The required geometric locus of points is the line $D C$.
72. In a circle, two mutually perpendicular diameters $A C$ and $B D$ are drawn. Let $P$ be an arbitrary point on the circle, and $P A$ intersects $B D$ at point $E$. A line passing through $E$ parallel to $A C$ intersects the line $P B$ at point $M$. Find the geometric locus of points $M$.