[alogo] Square construction

To construct a square ABCD given two points {E,F} on the diagonals BD, AC and two points {G,H} on two opposite sides AB, CD.

[0_0] [0_1] [0_2]
[1_0] [1_1] [1_2]

The circle with diameter EF has an arc bisected at I by the bisector of the diagonals, which pass also from the middle of GH. Since I, J are constructible from the data, the direction of the parallel sides AB, CD is known, as well as the location of the center O of the square. There are two solutions, since I can be selected on either side of EF.

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