How to rotate rectangular component such that two edges are touching outer rectangle

Why it does not work with both the “source” endpoint and the target endpoint being in the same context? SketchUp can’t inference one endpoint of an edge towards the other endpoint (same context). Nor can it drop one endpoint of a curve onto the endpoint on the other side of the curve (same context). That is basicly what you have been trying to do in your first attempt.
Grouping the smaller rectangle leaves the pie arc and its endpoint in tact.

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