| 单词 | radical circle |
| 释义 | > as lemmasradical circle radical circle n. [after French cercle radical (L. Gaultier 1813, in Jrnl. de l'École Polytechnique 9 131)] Geometry †(a) (in a system of circles drawn on a sphere whose planes intersect in a common line) the circle whose plane passes through the centre of the sphere (obsolete); (b) the circle whose centre is the radical centre of three given circles and which intersects each circle orthogonally. ΚΠ 1889 J. Casey Spherical Trigonom. 101 The circle of the system S, whose plane passes through the centre of the sphere, is called the radical circle of the system. 1927 Amer. Math. Monthly 34 357 The special cases are (1) O3c; (2) P1O2c; (3) P2Oc. The solution in each case is the radical circle. 1992 H. Eves Fund. Mod. Elem. Geom. 48 Show that if the radical center of three circles with noncollinear centers is exterior to each of the three circles, it is the center of a circle orthogonal to all three circles. (This circle is called the radical circle of the three circles.) < as lemmas |
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