Squaring the circle the circular arc b around O with radius , it results S'. Bisect the line segment in D and draw the semicircle b over D. Draw a straight line from O through C up to the semicircle b, it cuts b in E. The line segment is the mean proportional between and , also called geometric mean. Extend the line segment beyond O and transfer twice more, it results F and A, and thus the length of the line segment with the above described approximation value of formula_3, the half circumference of the circle. Bisect the line segment in G
Director circle ellipse. The Apollonius circle, the locus of points "X" such that the ratio of distances of "X" to two foci "P" and "P" is a fixed constant "r", is another special case, with "w" = 1, "w" = −"r", and "C" = 0. In the case of a parabola the director circle degenerates to a straight line, the directrix of the parabola. Director circle In geometry, the director circle of an ellipse or hyperbola (also called the orthoptic circle or Fermat–Apollonius circle) is a circle consisting of all points where two perpendicular tangent lines to the ellipse or hyperbola cross