Suppose you have the length of the circular arc AB, in addition to the coordinates of A and B. Is this information sufficient to draw the arc (i.e. find its center point)?
2026-03-25 07:48:22.1774424902
Is it possible to identify a circular arc given its length and two of its endpoints?
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It is sufficient except for an ambiguity of which side of the line segment $AB$ the center lies on. The center lies on the bisector of $AB$. If $r$ is the radius of the circle, $L$ is the length of the arc, $\theta$ is the angle at the center subtended by $AB$, $d$ is the length of $AB$ we have $$L=r\theta\\d=2r\sin\left (\frac \theta 2\right)$$ and we can solve these numerically to get $r, \theta$. This lets you find possible points for the center.
A figure is below. My $B,C$ are your $A,B$.