Question 9
Let $P_1P_2...P_n$ be a polygon inscribed in a circle and $Q$ a point outside the plane of the circle. Let $\beta_i$ be the plane perpendicular to $QP_i$ and passing through $P_i$, $i = 1, 2, ..., n$. Prove that the intersection of all planes $\beta_i$ is a point.