I have an arc which is intersecting with main line. how to automatically rotate the arc so that it is tangent to the line?
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Is this a really a grasshopper problem ?
your definition is empty.
with standard Rhino commands this is just a question of correct osnap::
_Rotate (snap to the Endpoint / red cross in your screenshot)
for the Second reference point use
_PerpendicularFrom (pick the long line, again the red cross point, a point on the target direction)
if you want to do it with grasshopper - you should create the arc already in the desired / final position.
To get a grasshopper - answer - share the way the 180-Degree-Arc with the closing segment got created.
kind regards -tom