Category:Inverse of Circle Not Through Inversion Center

This category contains pages concerning Inverse of Circle Not Through Inversion Center:

Let $\CC$ be a circle in the plane on center $O$.

Let $T : X \to Y$ be an inversive transformation with $\CC$ as the inversion circle.

Then $O$ is the inversion center.

Let $K$ be an arbitrary circle distinct from $\CC$ and not through $O$.

Then the image under $T$ of all the points on $K$ lie on the same circle, distinct from both $K$ and $\CC$.