Among the conditions used are the angular nature and among them the orthogonality.
Given the circles coplanarias, infinity simply set the circumferences that intersect orthogonally are grouped into a named set corradicales beam circumferences; These circles are centered on a line called radical axis.
The radical axis of two circles is the locus of points in the plane
- which are centers of circles orthogonal tells circles
- having equal power tells about the circumferences
- from which can be drawn equal length segments tangent to the circumferences
To determine this locus, radical axis, we will rely on a shape analysis comprises two circumferences which are orthogonally intersected by the desired.
We see triangles that meets, applying Pythagoras, the following relationships:
from which we can obtain
as we have seen in studying the locus of the difference of squares of distances from two fixed points, is a straight. This line is called radical axis of two circles.
Radical center of three circles
We see that by imposing two restrictions of orthogonality is determined a locus for the centers of the solutions that meet. If we introduce a third condition we obtain a unique solution we can get through the aforementioned intersection loci.
The CR radical center three coplanar circles is a point in its plane:
- is intersection of the three axes of the circumferences radicals
- has equal power with respect to these circles
- is center circle orthogonal to these circles
- from which can be drawn tangent segments of equal length to the three circles