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Just speculation on my part, but since you know two of the planes it's going to be in couldn't you simply treat it as a 1/2 circle & find the line at which 1/2 the area is above & 1/2 is below?

[EDIT]Even easier, treat it as a 1/4 circle & you only have to deal with one quadrant...[/EDIT]

Viper GTS
 
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