How is orthogonality between a line and a circle most simply defined?

Question

I was asked to show that if I have a generalized circle C, and two points not in C, then every circle going through these two points is orthogonal to C iff these two points are symmetric. Since I haven't come by anything yet but still have a hard time understanding the concept: is orthogonality between a line and a circle means the line halves the circle? How can one make sure it would stay this way for every generalized circle? Is that mobius? I could really use a guidance.

Answer 1

I give you a partial answer. When the radii of two circles are perpendicular or radius of one circle is perpendicular to other radius or when radius of one acts as a tangent for other or vice versa then the pair of circles is said to be orthogonal. Orthogonality depends upn number of intersection points between circles.

Answer 2

Try to imagine them as circles on the surface of a sphere if you want to visualize them.

Thus, the orthogonality is just treated as circles