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Timeline for Function describing two circles

Current License: CC BY-SA 4.0

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Mar 2, 2022 at 21:00 answer added Ethan Bolker timeline score: 0
Mar 2, 2022 at 19:40 comment added Googlebot @EthanBolker my question is pure math. I look to understand how we merge two circles. The examples from physics only aimed to compensate for my inability to express my question in math language.
Mar 2, 2022 at 19:13 comment added Ethan Bolker The extra information is both good and bad news. I now know the kind of answer you want. But without more explicit assumptions about the physics I think the question can't be answered. It might help if you edit the question to tell us how you expect to use any answer you get.
Mar 2, 2022 at 18:00 comment added Googlebot @EthanBolker no I do not have any equation. I added some physical examples to clarify my question.
Mar 2, 2022 at 17:59 history edited Googlebot CC BY-SA 4.0
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Mar 2, 2022 at 16:28 comment added Ethan Bolker Please edit the question to clarify. Do you have equations for the circles? The blue line is a segment of the common tangent. Yes, it can be parameterized by a variable that measures the distance of a point on it from one end. What is the red curve?
Mar 2, 2022 at 16:22 history edited Googlebot CC BY-SA 4.0
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Mar 2, 2022 at 16:14 history asked Googlebot CC BY-SA 4.0