How to extrude boss a half circle onto a lofted surface

I need to know if there is a feature that will allow me to extrude boss something onto the angle of a lofted edge so that it sits flush with the lofted edge surface rather than it leaving a gap

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As far as I understand from you question and images, I think Revolved Boss/Surface is the easiest way to get it done. Other options I can think of Lofted Boss/Surface or Swept Boss/Surface. It depends on what you want to do with it afterwards.

 
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When you are extruding, there is an option to apply a directional vector for the extrude. Set it to match the taper of your cone, and you should have what you are looking for.

 
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