According to various sources (e.g. [1, p. 102]), the terminology of the power of a point with respect to a circle is due to Steiner. His definition appears in most classical and contemporary geometry textbooks (to mention just a few references, see [2, 3, 4, 5]). The concept of the power of a point has been revisited not only in advanced Euclidean geometry, but also in computational geometry and other areas of mathematics.
In the current literature there are two different definitions of the power of a point with respect to a circle, which we study in detail in section 2. In the first half of the twentieth century there have been published several attempts to generalise the concept of power of the point to real algebraic curves.
