## Geometrical constructions with a ruler: given a fixed circle with its center |

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Annales de Mathematiques APOLLONIUS of Perga auxiliary circle belonging Berlin bisect center of similitude circle M2 circumscribed collinear common secant common tangents corresponding points cut the circle diagonals draw the diameter draw the line draw the rays drawn end-points equal powers EUCLID'S Elements EULER'S line example external fixed circle fixed point follows four points fourth harmonic point geometrische geometry given angle given circles given line given rational ratio H. G. ZEUTHEN H. J. S. SMITH harmonically conjugate internal center JACOB STEINER Leipzig lies midway line g line PQ line-locus line-segment locus LORENZO MASCHERONI MASCHERONI means meet the line midpoint orthocenter pairs of points Paris perpendicular plane point a parallel point Q points of intersection points with respect polar polygon PONCELET preceding problem proposed problem radii rectangle secant segment BC SERVOIS similarly situated points solution solved straight line tangents theorem three circles three points vertices