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How to draw a circle exactly center on a plane?

You need to constrain the circle to the curve, but first you need a point.

There are many ways to do this, but here is one way:
1. edit the circle sketch
2. draw a point where the sketch plane intersects the curve
- a. INSERT (top menu) + OPERATIONS + INTERSECT 3D ELEMENTS
- b. select the spline curve
3. constrain the circle centerpoint and the intersection point as COINCIDENT
4. add dimension for the size of the circle
5. EXIT the sketch
 
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When I'm modeling a tube or wire and I'm using a spline as the centerline; I build the sketch plane at one of the endpoints of the spline. Then I use that endpoint to center the circle.
 

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