Mathematics

A circle is completely determined by its center and radius. Since $C$ is fixed and $A$ is a specific point different from $C$, the distance from $C$ to $A$ is one fixed value—this becomes the radius. You can't choose a different radius and still have the circle pass through $A$, so there's only one possibility.

A circle is completely determined by its center and radius. Since $C$ is fixed and $A$ is a specific point different from $C$, the distance from $C$ to $A$ is one fixed value—this becomes the radius. You can't choose a different radius and still have the circle pass through $A$, so there's only one possibility.