Find arc centerpoint(x,y) with start(x,y) and end(x,y) in a conical helix

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arc centerpoint

Im trying to script drawing of a conical helix in 3D software, and are stuck at the last arc when its not a full 180 degree arc.

I know(calculate) the arc startpoint and endpoint, but how do I find the arc centerpoint?

In illustration, arc centerpoint are x6.252 and y16.796

The software needs only coordinates to do the arc, so i dont use radius either, but i can find the radius by calculating a full 180 degree arc (R14617.447)

draw the arc with :
START pointA_x, pointA_y,
ARC center_x, center_y, pointB_x, pointB_y, cw

How do I calculate centerpoints (x6.252 and y16.796 ) ? do i need arc length?