Constructing a Parallelogram with a Given Diagonal

Construction Algorithm
1 Construct a line AC as a given diagonal of the parallelogram.
2 Construct M as a midpoint of the diagonal AC.
3
Construct a free line through M.
4 Construct a point B on the free line.
5 Construct a circle centered at M and has a circumference point B at the free line.
6 Generate the intersection points between the circle and the free line to find the fourth vertex D of the parallelogram.
7 Join up the four points A, B, C, and D to get the required parallelogram.
8 Switch to Move Mode. Pick a free element. Move it around to check your construction.
Construction Theorem
A parallelogram is a quadrilateral, in which diagonals bisect each other.
Please enable Java for an interactive construction (with Cinderella).