Equation of Tangent to Circle Centered at Origin

Theorem
Let $\CC$ be a circle whose radius is $r$ and whose center is at the origin of a Cartesian plane.

Let $P = \tuple {x_1, y_1}$ be a point on $\CC$.

Let $\TT$ be a tangent to $\CC$ passing through $P$.

Then $\TT$ can be defined by the equation:


 * $x x_1 + y y_1 = r^2$