208. 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 set of points $M$.
208. Consider the quadrilateral $D E P M . \widehat{D E M}=\widehat{D P M}=$ $=90^{\circ}$, hence this quadrilateral is cyclic. Therefore, $\widehat{D M E}=\widehat{D P E}=45^{\circ}$. The desired set is the line $D C$.

![](https://cdn.mathpix.com/cropped/2024_05_21_6282cf4a54d2a9633c48g-119.jpg?height=428&width=602&top_left_y=735&top_left_x=319)

Fig. 54.