Equations for tangent & normal at P2 of circle P1 P2 P3?

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Discussion Overview

The discussion revolves around determining the equations for the tangent and normal lines at point P2 on a circle defined by three points P1, P2, and P3 in three-dimensional coordinates. The focus is on the geometric relationships and constructions necessary to derive these lines.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant suggests that finding the center of the circle is the first step in determining the tangent and normal lines at P2.
  • Another participant notes that the center of the circle is not located on the lines connecting the points and questions the relationship of the center to the normals of the points.
  • A later reply proposes constructing the perpendicular bisectors of the lines between the points to find the center of the circle, stating that this center can be used to derive the normal line to the circle at P2.
  • This same reply indicates that the line from the center to P2 is normal to the circle at that point, and constructing a line perpendicular to this normal will yield the tangent line at P2.

Areas of Agreement / Disagreement

Participants appear to agree on the necessity of finding the center of the circle to derive the tangent and normal lines, but there are differing views on the specifics of how to approach this, particularly regarding the relationship between the center and the normals.

Contextual Notes

There are assumptions regarding the geometric properties of circles and the methods for finding perpendicular bisectors that are not fully explored or defined in the discussion.

CosmicVoyager
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Greetings,

Given three points P1 P2 P3 on a circle in x,y,z coordinates, I am trying to figure out how to get the tangent and normal at P2.

Anyone?

Thanks
 
Last edited:
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Hi CosmicVoyager! :smile:

Well, that means you first need to find the centre of the circle …

what lines do you think that will be on? :wink:​
 
tiny-tim said:
Hi CosmicVoyager! :smile:

Well, that means you first need to find the centre of the circle …

what lines do you think that will be on? :wink:​

The center of the circle won't be on any of the lines between the points. It is opposite the their normals?
 
If you construct the perpendicular bisectors of the lines between the points, they will intersect at the center of the circle.

Once you know that, construct the line from that center to each point. That line itself will be normal to the circle at the point. Constructing the line perpendicular to that line at the point gives you the tangent to the circle at that point.
 

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