Power center (geometry)

In geometry, the power center of three circles, also called the radical center, is the intersection point of the three radical axes of the pairs of circles.

Similarly, for every point on the radical axis of circles 2 and 3, the powers must be equal, h2 = h3.

Therefore, at the intersection point of these two lines, all three powers must be equal, h1 = h2 = h3.

Since this implies that h1 = h3, this point must also lie on the radical axis of circles 1 and 3.

It has an important role in a solution to Apollonius' problem published by Joseph Diaz Gergonne in 1814.