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Break circle where user clicks

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Hi, I'm having some issues right now with breaking a circle where a user clicks. The way I'm currently doing it (which works for straight polylines) is to take the Feature object and cast it to IFeatureEdit2. Afterwards I use the .SplitWithUpdate(IPoint userPoint) method on the FeatureEdit2 object.

However when I try this with a Circle feature (clicking on point 1) it creates two breaks and makes two arcs as in the image attached. I would like it to just keep one arc with a break at the point the user clicked and no where else. This way I could click on point2 later and have two arcs split by the two polylines crossing them and select/delete whatever one I no longer need.

When I click for the second time to break the line again it works as expected, however I'm left with 3 arcs instead of the 2 I want.
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