KöMaL 2016 B4814

Let $P$ be a given point in the interior of a sphere. Consider the pairwise perpendicular planes $S_1$, $S_2$ and $S_3$ that intersect at $P$. Show that the sum of the areas of the circles cut out of the planes by the sphere is independent of the choice of the planes $S_1$, $S_2$ and $S_3$.