Question 35
$S$ and $S'$ are two intersecting spheres. The line $BXB'$ is parallel to the line of centers, where $B$ is a point on $S$, $B'$ is a point on $S'$, and $X$ lies on both spheres. $A$ is another point on $S$, and $A'$ is another point on $S'$ such that the line $AA'$ has a point on both spheres. Show that the segments $AB$ and $A'B'$ have equal projections on the line $AA'$.