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If the radii are equal, the radical axis is the line segment bisector of M 1, M 2. In any case the radical axis is a line perpendicular to ¯. On notations. The notation radical axis was used by the French mathematician M. Chasles as axe radical. [1] J.V. Poncelet used chorde ideale. [2]
The radical axis of a pair of circles is defined as the set of points that have equal power h with respect to both circles. For example, for every point P on the radical axis of circles 1 and 2, the powers to each circle are equal: h 1 = h 2. Similarly, for every point on the radical axis of circles 2 and 3, the powers must be equal, h 2 = h 3.
The radical axis of two intersecting circles. The power diagram of the two circles is the partition of the plane into two halfplanes formed by this line. In the case n = 2, the power diagram consists of two halfplanes, separated by a line called the radical axis or chordale of the two circles. Along the radical axis, both circles have equal power.
A pencil of circles (or coaxial system) is the set of all circles in the plane with the same radical axis. [9] To be inclusive, concentric circles are said to have the line at infinity as a radical axis. There are five types of pencils of circles, [10] the two families of Apollonian circles in the illustration above represent two of them.
The line connecting these common intersection points is the radical axis for all three circles. The two isodynamic points are inverses of each other relative to the circumcircle of the triangle. The centers of these three circles fall on a single line (the Lemoine line). This line is perpendicular to the radical axis, which is the line ...
The set of all points with () = is a line called radical axis. It contains possible common points of the circles and is perpendicular to line O 1 O 2 ¯ {\displaystyle {\overline {O_{1}O_{2}}}} . Secants theorem, chords theorem: common proof
Figure 1: The point O is an external homothetic center for the two triangles. The size of each figure is proportional to its distance from the homothetic center. In geometry, a homothetic center (also called a center of similarity or a center of similitude) is a point from which at least two geometrically similar figures can be seen as a dilation or contraction of one another.
In geometry and linear algebra, a principal axis is a certain line in a Euclidean space associated with a ellipsoid or hyperboloid, generalizing the major and minor axes of an ellipse or hyperbola. The principal axis theorem states that the principal axes are perpendicular , and gives a constructive procedure for finding them.