tangent perpendicular to a circle, not just a radius

[emhines]

I have never seen this before. I know that a tangent line is perpendicular to a line drawn through the center of the circle at the point of tangency. A curriculum that I am reading states that :
"A tangent line is perpendicular to a circle at the point of tangency."
While I agree that the tangent line is perpendicular to the line that connects the center to the circle at the point of tangency, I cannot find any other reference that states that the line is perpendicular to the actual circle.

 

[masters]

I have never seen this before. I know that a tangent line is perpendicular to a line drawn through the center of the circle at the point of tangency. A curriculum that I am reading states that :
"A tangent line is perpendicular to a circle at the point of tangency."
While I agree that the tangent line is perpendicular to the line that connects the center to the circle at the point of tangency, I cannot find any other reference that states that the line is perpendicular to the actual circle.

Hi emhines,

In my opinion, that is a poorly worded statement. Lines are perpendicular to other lines, not circles. The intent, I believe, was to say "a tangent line is perpendicular to a radius (diameter) at the point of tangency."

 

[pka]

"A tangent line is perpendicular to a circle at the point of tangency."
While I agree that the tangent line is perpendicular to the line that connects the center to the circle at the point of tangency, I cannot find any other reference that states that the line is perpendicular to the actual circle.

While I agree that "A tangent line is perpendicular to a circle at the point of tangency." is an absurd statement, it does not follow that “line is perpendicular to the actual circle” is also absurd.

In fact, there is a well define idea “of a line being perpendicular to a curve”.
It is call the normal at a point. The normal at a point is the line perpendicular to the tangent at the point.
Thus the normal to a point on the circle is simply the line determined by the point and the center of the circle. That line is said to be perpendicular to the circle.