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Four rods of equal lengths are hinged at their endpoints to form a rhombus ABCD.

 

Keeping AB fixed, CD is free to move in the plane with the angle BAD between 0 and 180 degrees.

What is the locus (or path) of the point D?

What is the locus of Y, the point one third of the way along DC? (DY:YC = 1:2)