How do I calculate arc angle between two points on a circle?

Given a circle with a known center point and two points on the circle (开发者_如何学Cthus known radius), how do I determine the angle of the minimum arc between the two points on the circle?

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Turn the center to the two points into a pair of vectors, then shove through this.

So, cos^-1 ((x₁x₂ + y₁y₂ + z₁z₂) / r²).