Is there a version of the central angle theorem that applies to spheres and solid angles? The central angle theorem (in one formulation) tells us that if C is a circle containing the point p and C' is a circle centered at p, then projection from C to C' through p halves all angles. if S is a sphere containing the point p and S' is a sphere centered at p, does projection from S to S' through p halve all solid angles? By the way, I spent about three minutes fruitlessly searching the internet for an answer, and I figure that that's enough, since one of you has probably thought about this before and can answer my question in under three minutes. But if some of you think that I (and other posters) should do more googling before we post our questions, please let me know. Jim Propp