you not only need to find the point O, but also, more importantly, you need to make sure that OC=OD, which is the radius of the circle.
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In your statement, although "O can move on this circle and
So, there is one, and only one, point O on segment AD, from which you can draw a cirlce with radius OD (or OC) that passes all the three points: C, D, B.