Radical axis

From AoPSWiki

The radical axis of two circles $\omega_1, \omega_2$ is defined as the locus of the points $P$ such that the power of $P$ with respect to $\omega_1, \omega_2$ are equal. If $O_i, r_i$ are the center and radius of $\omega_i$ , then we say that for any point $P$ on the radical axis,

The radical axis is a line. If the two circles intersect at two common points, their radical axis is the line through these two points (because the power of each of the common points is $0$ ); if they intersect at one point, their radical axis is the common internal tangent.

The three pairwise radical axes of three circles concur at a point, called the radical center.

Personal tools

Navigation

Search

Toolbox

Radical axis

From AoPSWiki