Constructing a Square with a Given Center*

Construction Algorithm
1 Construct a point M as a center of the square.
2 Construct a point A on the construction area 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 circle at C.
6 Construct a perpendicular line through the point M.
7 Generate the intersection points between the free line and the circle at B and D.
8 Join up the four points A, B, C, and D to get the required square.
9 Switch to Move Mode. Pick a free element. Move it around to check your construction.

Construction Theorem

The two diagonals of the square are perpendicular to each other, bisect each other, and equal in length.

Please enable Java for an interactive construction (with Cinderella).
Please enable Java for an interactive construction (with Cinderella).

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