On strict strong constructibility with a compass alone
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We show that every point in the plane which can be constructed by a compass and a ruler, given a setS of points, can be constructed using a compass alone so that the following restriction is met. LetO andK be two arbitrarily chosen distinct points ofS. Then every point is obtained as a proper intersection of two circles that are either completely symmetrical with respect to the lineOK or have both their centers on this line.
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