Is radius perpendicular to the circle?

[pavelcherepan]

Hi everyone! Stupid question in the topic. Obviously, radius is perpendicular to a tangent at a point of intersection, but can it be said that radius is perpendicular to the circle itself? Does such statement even make sense?

[LaurieAG]

An axle is perpendicular to the plane of a circular wheel but it is not quite a radius.

[pavelcherepan]

5 minutes ago, LaurieAG said:

An axle is perpendicular to the plane of a circular wheel but it is not quite a radius.

Why is the axle not quite radius if it does connect the center of a circle to its perimeter?

[DrP]

2 hours ago, pavelcherepan said:

Why is the axle not quite radius if it does connect the center of a circle to its perimeter?

It doesn't connect to the perimeter. It is perpendicular to the plane of the circle through the centre. The axle would then be perpendicular to the plane of the circle itself....  I don't see the radius being so - it is in plane with the circle and not perpendicular to it.

 

[pavelcherepan]

25 minutes ago, DrP said:

It doesn't connect to the perimeter. It is perpendicular to the plane of the circle through the centre.

Sorry, I don't follow. Could you elaborate please?

[DrP]

The axle goes through the centre of the circle...  if drawn in 2d on a piece of paper the axle line goes straight up through the centre of the circle out of the page - perpendicular to the plane of the circle and the page it is on. It never touches the perimeter.  The radius is drawn from the centre of the circle to the perimeter...  it is in plane with the circle and the paper it is drawn on. It is parallel to the page - not perpendicular to it.

So - the radius is parallel to the plane of the circle - or in plane with it. The axle is perpendicular to the plane of the circle.

Maybe you could say it was perpendicular to the circumference at the point it meets it?   

[pavelcherepan]

4 minutes ago, DrP said:

Maybe you could say it was perpendicular to the circumference at the point it meets it?   

Yeah, that was what I was going for. Is that the case?

[DrP]

1 minute ago, pavelcherepan said:

Yeah, that was what I was going for. Is that the case?

That's basically the same as it being perp to the tangent though, no? I don't think you can say it is perpendicular to the circle imo. Being perpendicular to just one tiny infinitesimally small point on the circumference doesn't make it perp to the whole thing.  The axle IS perp to the whole thing though like LaurieAG suggested.

 

 

[mathematic]

In general, when talking about angle between intersecting lines (curves) the angle is between tangents at the point of intersection.  Radius is perpendicular to tangent, therefore perpendicular to circumference at that point.