Constructing a Rhombus with a Given Center*

Construction Algorithm
1 Construct a point M as a center of the rhombus.
2 Construct a point A on the construction area that is next to the point M.
3
Construct the line that connects the two points A and M.
4 Construct a circle centered at M and has a radius AM.
5 Generate the intersection point between the line AM and the constructed circle at C.
6 Construct a perpendicular line to the line AC through the point M.
7 Add a point B on the perpendicular line.
8 Construct a circle centered at M and has a radius BM.
9 Generate the intersection point D between the perpendicular line and the second circle.
10 Join up the four points A, B, C, and D to get the required rhombus.
11 Switch to Move Mode. Pick a free element. Move it around to check your construction.
Construction Theorem
The two diagonals of a rhombus are perpendicular and bisect each other.
Please enable Java for an interactive construction (with Cinderella).

*Center of the rhombus is the intersection point of its diagonals.