There are multiple ways to modify an object in your drawing. If the object is a rectangle, an ellipse, a star or a spiral, i.e. a geometrical shape drawn with one of the shape tools, then this object is a shape, and not a path. Shapes can only be modified by dragging their specific handles. In contrast to shapes, you must use tools that are meant for modifying paths, if you want to edit a path. Shapes can be converted into paths, so the path tools can then be used with them.
To convert a shape into a path:
The Boolean Operations work on paths, or they try to convert the selected objects to paths before they compute the result. All these operations need at least 2 convertible objects or paths, which will be combined following specific rules.
To use these operations, select the two (or more) objects, and then select the option of your choice in the Path menu. The result will immediately appear on the canvas - if it doesn't, read the error message that will appear in the status bar, at the bottom of the Inkscape window, to find out about the reason for the failure.
Unioning a triangle and a square gives a house.
Difference between a rectangle and a house creates an opening for the door.
Two overlapping ellipses.
Intersection between the two ellipses.
Exclusion between the two ellipses.
Someone has drawn a path with the pencil tool (with the setting of shape: Ellipse) on the orange ellipse.
Move apart and combine (to form a single path composed of two subpaths).
Break Apart separates all subpaths into independent objects.
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