Can anyone help a trig simpleton bisect an angle in POVRay?

If I have three points in space (A, B & C), how can I

1) Find the angle of ABC

2) Find the point (D) which lies at a point bisecting an arc AC so that
line DB equals line AB equals line CB ?

I'd like this to work for any three arbitrary points, so I can create a
rounded mesh "box" macro for "boxes" that aren't necessarily regular.
Any help would be appreciated.

TIA,

DeanZ

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