How do you intersect a line into the middle of a separate line to create closed shapes?

I am sure this is easy but I cannot figure it out and have not been able to find an explanation showing what I am trying here.

I am staring with a line. I want to draw a new line from a point on that line, say 1/4 the way from one end of that line, draw a basic shape, say half circle, and have the second end of this drawn line come back to the original line and connect 1/4 away from the opposite end of the original line. I want these lines to connect in a way so that it closes the shape and for the whole piece to be one line/shape.

I have been able to connect ends of lines to each other to create continuous lines or to close shapes. But I cannot figure out how to create a shape off of the side of another shape.

I have attached a file I was trying to make this work with. Any help would be greatly appreciated!

Test Closing Shapes 1-12-2025.lbrn2 (12.6 KB)

Nodes cannot connect more than 2 lines - a 3 way or 4 way intersection will not close.

Step 1 - close the first shape

Use Boolean tools to meld the two shapes into one:

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Thank you! I really appreciate the help!

You can use the Trim Shapes Tool and remove the highlighted line.

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