2016 AIME II Problem 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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.