THEOREM OF THE DAY: The Power of a Point Theorem

Theorem

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 

$h = |s^2 − r^2|$. 

Click on the image.

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