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.