Question 14
Equilateral $\triangle ABC$ has side length $600.$ Points $P$ and $Q$ lie outside the plane of $\triangle ABC$ and are on opposite sides of the plane. Furthermore, $PA = PB = PC,$ and $QA = QB = QC,$ and the planes of $\triangle PAB$ and $\triangle QAB$ form a $120^\circ$ dihedral angle (the angle between the two planes). There is a point $O$ whose distance from each of $A,$ $B,$ $C,$ $P,$ and $Q$ is $d.$ Find $d.$