page_title: Radical axis
section_title: Definition and general properties
hierarchical_section_title: Radical axis / Definition and general properties
context_page_description: The radical axis of two non-concentric circles is a line defined by the two circles, perpendicular to the line connecting the centers of the circles. If the circles cross, their radical axis is the line through their two crossing points, and if they are tangent, it is their line of tangency. For two disjoint circles, the radical axis is the locus of points at which tangents drawn to both circles have equal lengths. The radical axis is always a straight line and always perpendicular to the line connecting the centers of the circles.
  For any point P on the radical axis, there is a unique circle centered on P that intersects both circles at right angles; conversely, the center of any circle that cuts both circles orthogonally must lie on the radical axis. In technical language, each point P on the radical axis has the same power with respect to both circles
  where r₁ and r₂ are the radii of the two circles, d₁ and d₂ are distances from P to the centers of the two circles, and R is the radius of the unique orthogonal circle centered on P.
caption: If the two circles intersect, the radical axis is the secant line corresponding to their common chord.