There is a concept of a "power of a point with respect to a circle".
If one has a point which is distance $d$ away from the centre of some circle and that circle has radius $r$ then the power of this point is said to be $d^2-r^2$.
I am unable to find much about the history of this concept except that it originated somewhere in mid $19$th century. Does anybody know why this concept was useful and why it developed?
On
Note that the definition (and the equality) holds if the line is tangent to the circle.
E.g., the line may intersect $P$ and only one point $T$ of the circle (so it's a tangent line). In that case, $PT^2$ remains constant and equal to $|r^2-d^2|$, where $d$ is the distance from $P$ to $T$, that is, the minimum distance from $P$ to the circle in the intersecting line.
The term "power of a point" was first defined by Jakob Steiner in 1826 in a work called "A Few Geometrical Observations." A brief article on this subject can be found here.
Steiner observed that if we consider a circle of radius $r$ and a point $P$ not on the circle, and examine any line which which intersects $P$ and two points on the circle, $A$ and $B$, then we find that $AP\cdot PB$ is constant (that is, the product of the lengths of those two segments is constant) for any $P$ inside or outside the circle. This constant value is $|r^2 - d^2|$ with $d$ being the minimum distance from $P$ to the circle. One way in which this idea is used is in defining the radical axis of two circles: a point is on the radical axis of two circles if it has the same power with respect to both of them.