Find a center of circle given a point and radius

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Discussion Overview

The discussion revolves around the problem of finding the center of a circle given a point that is described as tangent to the circle and a specified radius. The scope includes mathematical reasoning and conceptual clarification regarding the definitions involved.

Discussion Character

  • Debate/contested, Conceptual clarification, Mathematical reasoning

Main Points Raised

  • CG asks how to find the center of a circle given a point that is tangent to the circle and the radius.
  • One participant questions the meaning of "tangent," asking whether it refers to any point on a tangent line or specifically the point of contact between the tangent and the circle.
  • Another participant suggests that the problem does not have a single solution, proposing that the locus of possible centers forms a circle centered at the given point.
  • A different participant asserts that a point cannot be tangent to a circle, indicating a potential misunderstanding in CG's question.

Areas of Agreement / Disagreement

Participants express differing interpretations of the term "tangent" and the nature of the problem, indicating that multiple competing views remain without a consensus on the definitions or the approach to the problem.

Contextual Notes

There are unresolved assumptions regarding the definitions of tangent points and the implications for the solution space, which may affect the interpretation of the problem.

cg76
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Hi all,

How do I find the center of a circle given a point (tangent to the circle) and the radius.

Thanks,
CG
 
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cg76 said:
Hi all,

How do I find the center of a circle given a point (tangent to the circle) and the radius.

Thanks,
CG

What does that mean? Any point on a tangent or the point of contact of tangent and circle?
 
This problem does not have a single solution, instead, the solution of where the center of the circle could be is a circle in itself; in other words, the locus of the solution is a circle with center at the point given.
 
cg76 said:
Hi all,

How do I find the center of a circle given a point (tangent to the circle) and the radius.

Thanks,
CG

A point cannot be tangent to a circle, so it's not clear what you are talking about
 

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