How to use Radical-axis in a sentence
A system coaxal with the two given circles is readily constructed by describing circles through the common points on the radical axis and any third point; the minimum circle of the system is obviously that which has the common chord of intersection for diameter, the maximum is the radical axis - considered as a circle of infinite radius.
In the case of two non-intersecting circles it may be shown that the radical axis has the same metrical relations to the line of centres.
There are several methods of constructing the radical axis in this case.
To construct circles coaxal with the two given circles, draw the tangent, say XR, from X, the point where the radical axis intersects the line of centres, to one of the given circles, and with centre X and radius XR describe a circle.
The radical axis is x = o, and it may be shown that the length of the tangent from a point (o, h) is h 2 k 2, i.e.Advertisement
The construction in fact is, join the two points in which the third circle meets the first arc, and join also the two points in which the third circle meets the second arc, and from the point of intersection of the two joining lines, let fall a perpendicular on the line joining the centre of the two circles; this perpendicular (considered as an indefinite line) is what Gaultier terms the " radical axis of the two circles "; it is a line determined by a real construction and itself always real; and by what precedes it is the line joining two (real or imaginary, as the case may be) intersections of the given circles.
The intersections which lie on the radical axis are two out of the four intersections of the two circles.