The Theorem of the Day: The Power of a Point Theorem

The Power of a Point Theorem In the Euclidean plane, let $C$ be a circle of radius $r$. Let $P$ be a point whose distance from the centre of $C$ is $s$, and define the power of $P$ relative to $C$ to be the constant $h = |s_2 − r_2|$. 

Then for any line through $P$ intersecting $C$, $h$ is equal to the product of the distances from $P$ to its points of intersection with $C$.

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