Tangent and normal vectors at a point on a circle through three points

[CosmicVoyager]

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

 

[tiny-tim]

Hi CosmicVoyager!

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

what lines do you think that will be on? ​

 

[CosmicVoyager]

Hi CosmicVoyager!

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

what lines do you think that will be on? ​

The center of the circle won't be on any of the lines between the points. It is opposite the their normals?

 

[HallsofIvy]

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.