Radical axis

Of the power lines ( power line chordal ) of two circuits is defined as the locus (the quantity ) of all points on the power match with respect to the two circles. Are the circles given by their centers and as well as their radii, and so the power is precisely consists exactly of the points for which

Applies. The power line is defined only if the given circles are not concentric, that have no matching center.

Properties

• The potency precisely two circles is perpendicular to the connecting line of the two circle centers.

For two intersecting circles (case 3) the potency straight line passes through the two points of intersection. If the two circles touch ( cases 2 and 4), the true power of straight line with the common tangent.

• The distances between the power line of the two circular center points are given by:

This call and the radii; stands for the distance of the center points.

• For the points of the power line that are outside of the given channels, the sections are of equal length tangent to both circles.

• The potency precisely two circles is the set of centers of all circles which intersect the given circles at right angles.

• If three circles given, under which no two are concentric, so there are three power lines (one to two circles ). If the centers of the given circles do not lie on a straight line, the power lines intersect at a point ( engl. radical center), in the center of the circle that intersects the given circles at right angles (English radical circle ).