The origin of Arrhenius circle: Arrhenius circle is also called apollonius circle. If two points A and B on the plane are known, then the locus of all points P satisfying Pa = k Pb (k ≠ 1) is a circle. This trajectory was first discovered by the ancient Greek mathematician apollonius, so it is called "Arrhenius Circle".

Archimedes Circle Theorem: The locus of a point whose distance to two fixed points is constant (not equal to 1) is a circle (Archimedes Circle).

The maximum value of "PA+K Pb" is a hot and difficult issue in the senior high school entrance examination in recent years. When the value of k is 1, it can be transformed into the shortest sum problem of "PA+PB", which can be treated by our common "general horse drinking problem" model, that is, it can be transformed into an axisymmetric problem.