Why not just draw a new arc with the 2-point arc tool? The arc will start off tangent to the first segment and will pull an arc all the way to the endpoint of the last segment. It will (should) overlay the original arc.
You can read the length in the measurement box at the lower right corner of the screen without clicking the second point.
The OP wants to have/create an edge of equal length as the true length of a drawn arc, measured along the arc, not along all the segments, nor straight between both ends of the arc.
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Been thinking about this (do you smell smoke?)
Not actually a solution to the question, but isn’t this actually the circumference of a circle, with a certain part of the circle missing?
Just a random, potentially useless thought.
Must be some applicable math?
The math is in my reply earlier in this topic.
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The length of an arc is a fraction of the circumference of a circle with the same radius but in order to calculate it you’d need to know how many degrees of arc there is and then calculate the difference.
That’s what I was thinking, that is all. Over and out.