Power of a point
Relative distance of a point from a circle
Power of a point
In elementary plane geometry, the power of a point is a real number that reflects the relative distance of a given point from a given circle. It was introduced by Jakob Steiner in 1826. Specifically, the power Π ( P ) {\displaystyle \Pi (P)} of a point P {\displaystyle P} with respect to a circle c {\displaystyle c} with center O {\displaystyle O} and radius r {\displaystyle r} is defined by Π ( P ) = | P O | 2 − r 2 . {\displaystyle \Pi (P)=|PO|^{2}-r^{2}.} If...
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