Question 41
Let $O \cdot X Y Z$ be a trirectangular trihedron with vertex $O$ and edges $X$, $Y$ and $Z$. On the edge $Z$ a point $C$ is set such that $O C = c$. About $X$ and $Y$, variable points $P$ and $Q$ are considered, respectively, so that $O P + O Q$ is a constant given $k$. For each pair of points $P$ and $Q$, the four points $O$, $C$, $P$ and $Q$ determine a sphere, the center of which $W$ is projected onto the plane $O X Y$. Reason what the geometric locus of that projection is. Also reason what the locus of $W$ is.