Circular Inversion - reupload

Inversion is a very powerful tool for the problems involving circles. This also a non-Euclidean geometry, which is a very interesting subject.
*I have made some typo in the last video, so I decided to reupload it.*
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Music:
Outgoing Hikikomori - Stargazing
• Outgoing Hikikomori - ...
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[@Achill101]

Thank you, thank you, thank you. I was looking for a geometric proof in KZbin that a circle inverted at a circle results in another circle, and you delivered. Now, inversion at a circle makes so much sense to me. (Straight lines are just limits of inverted circles moved to origin.)

[@Achill101]

Do I understand it correctly that if A and C are on a straight line through the origin of the inversion and on the same side of the origin, then the angle, under which AC is seen from a arbitrary point B (that is not the origin), ABC, is the same angle as the one, under which the inverted section A'C' is seen from the inverted point B', C'B'A'? (Just with reversed orientation.) . . . What about if A and C are on the straight line through the origin but on different sides of the origin? Would the new angle be something like 360deg-OldAngle or similar? Which, for circles, would turn 90deg into 270deg of the outer angle?

[@ergasterr]

First comment on this re-upload. So Sir/Madam how do you make this beauty of a kind (animation). I would love to see a behind the scenes or making of it(probably others too).

[@doubledonut9313]

I am using JavaScript and After effects to make these videos. for the making of part, it was just me try to get the expression( basically JavaScript in after effects) working in 2 hours and using 10 hours to debugs and find out the typos in the scripts

[@federicovolpe3389]

Very nice animation 👍