99-100 Reflection over a Circle

Gave this task to a student who had already seen the BEAM problems. Can you come up with a strategy for reflecting a point over a circle (inversion through a circle)? Each point outside the circle has to map to one and only one point inside, and vice versa.
Here’s his thinking on a whiteboard:

He is using the angle between the two tangents to uniquely map the image inside (and outside if necessary) the circle.

Here’s his desmos sketch. Really cool.

 

 

dan

 

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