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.
On
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.
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.