Power center (geometry)

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This article is about the geometrical term. For large retail shopping centres which have a similar name, see power centre.

In geometry, the power center of three circles, also called the radical center, is the intersection point of the three radical lines. Radical lines are usually chords connecting the intersection points of a pair of circles, but can be generalized as dividing non-intersecting circles into equal circle power. If three circles are the same size and symmetrically distributed, the power center is the same as the geometric center. There is an interesting theorem that three such radical lines always meet at a single point (see radical axis).