 Power of a point

The power of a point $P$ relative to a circle with center $O$ and radius $r$ is $O{P}^2-r^2$. If a line through $P$ meets the circle at $A$ and $B$, the product of the directed distances $PA$ and $PB$ equals this quantity.

The "Power of a Point" theorem is a fundamental concept in geometry, particularly in the study of circles. It provides a relationship between the distances from a point to a circle and various segments created by lines related to that circle.