Radical axis
（重定向自Radical line）
![Figure 1. Illustration of the radical axis (red line) of two given circles (solid black). For any point P (blue) on the radical axis, a unique circle (dashed) can be drawn that is centered on that point and intersects both given circles at right angles, i.e., orthogonally. The point P has an equal power with respect to both given circles, because the tangents from P (blue lines) are radii of the orthogonal circle and thus have equal length.](/Images/godic/202502/05/Radical_axis_orthogonal_circles.svg1115.png")
![If the two circles intersect, the radical axis is the secant line corresponding to their common chord.](/Images/godic/202502/05/Radical_axis_intersecting_circles.svg1115.png")
![Figure 2: The radical center (orange point) is the center of the unique circle (also orange) that intersects three given circles at right angles.](/Images/godic/202502/05/Radical_center.svg1115.png")
![](/Images/godic/202502/05/Radical_axis_construction.svg1116.png")
The radical axis (or power line) of two circles is the locus of points at which tangents drawn to both circles have the same length. For any point P on the radical axis, there is a unique circle centered on P that intersects both circles at right angles (orthogonally); 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