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this is quite embarrasing but I've struggled with one shape for over 1 hour now. I have to draw a christmas sock icon. Something like that:

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I don't want to draw the lower part with free hand because an icon should be pixel perfect. So I'm trying to find out how to create the lower part of the sock with simple shapes. I've placed 2 shapes on top of each other:

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Now I need to unite them so everything looks smooth and perfect. I've tried to combine them with Shape Builder Tool and Unite in Pathfinder but the results are not correct. I've tried to change the dimensions of the circle and rectangle but nothing works.

There's probably a simple way of doing it but I can't figure it out by myself. Thank you for your help.

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In the example, it looks like you're missing the "heel" of the stocking shape, so you'll have to create a third shape or rethink the shapes you're using to create the stocking shape to accommodate this area. I'd recommend losing the circle and using two rounded rectangles. Once you have the structure built, use the Shape Builder Tool, Shift + M, or the Unite operation in the Pathfinder Window, Shift + Command + F9 or Window > Pathfinder to combine the overall shape:

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If you want some more control over the rounded corners of the final shape, try simplifying the pieces even more by using regular rectangles and edit corners after you combine by using the Direct Selection Tool, A, to select anchor points and round them accordingly with the round corner nodes that appear around the shape:

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Note: I prefer to build shapes with a Fill as opposed to a Stoke to have more control of how edges line up. If you're looking for "pixel perfection" you can line up shapes in Outline Mode Command + Y and it will more accurately represent where the fill ends rather that the stroke.

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