Analytic geometry | Circles | Elementary geometry
Radical axis
In geometry, the radical axis of two non-concentric circles is the set of points whose power with respect to the circles are equal. For this reason the radical axis is also called the power line or power bisector of the two circles. In detail: For two circles with centers and radii the powers of a point with respect to the circles are . Point belongs to the radical axis, if * . If the circles have two points in common, the radical axis is the common secant line of the circles. If point is outside the circles, has equal tangential distance to both the circles.If the radii are equal, the radical axis is the line segment bisector of .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. J.V. Poncelet used chorde ideale. J. Plücker introduced the term Chordale.J. Steiner called the radical axis line of equal powers (Linie der gleichen Potenzen) which led to power line (Potenzgerade). (Wikipedia).
