Erased square

I draw a square on the sand. On each of its sides, I put a stone.
Two days later, the stones didn't move, but the wind has blown away the square.
Could you find again the square, given the stones ? Solution

Extensions

Now I put the stones on the lines containing the sides.
Same problem. Solution

Details

New : The points are replaced by circles touching the square's sides
(That is to construct a square whose sides are tangent to 4 given circles)
And also : the square is replaced by a golden rectangle (ratio of sides = φ = (1 + √5)/2)
Details

Inverse

Now the inverse problem :
I draw 4 points at the vertices of a square on a paper. Then I draw 4 lines going through these points. Unfortunately, the lines having the same colour as the points, I can't see my points anymore ! And of course I didn't draw the square itself...
Could you find it ? Hint

Details

 

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