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I need to find the centre of a circle for which I have a segment with the bisection of the chord. I know the centre must lie on the perpendicular bisector, but I need to know how far down. I need to do this in Photoshop on a given image, so I can use compasses (arbitrary size circle in Photoshop) and straight edges (lines in Photoshop). Is there a way I can do this?

Thanks.

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    $\begingroup$ Just take a second cord and draw a second bisector, the center lies at the intersection of them. $\endgroup$ – Surb Jan 6 '15 at 10:21
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Hint If you take any two distinct cords, the center of the circle lies at the intersection of their respective bisectors.

NB This follows from the fact that there is a unique circle passing through three distincts points in the plane and the center of this circle must be at equal distance to all of these points.

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  • $\begingroup$ Note that you only need a compass and a ruler to draw a cord and its bisector. $\endgroup$ – Surb Jan 6 '15 at 10:26
  • $\begingroup$ Yes, I know; but I have only the one chord, the one on the segment. $\endgroup$ – Gary Jan 6 '15 at 10:45
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    $\begingroup$ @Gary what is the problem with choosing any other point on the circle and produce a second chord? $\endgroup$ – Surb Jan 6 '15 at 10:46
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I found the answer to my question here : http://www.cut-the-knot.org/do_you_know/compass13.shtml) This gives an answer using compass only; as I had the "luxury" of using a "straight edge" as well, I was able to simplify slightly.

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