Just an informal question out of curiosity.
Let's consider the simplest case of a circle, there is an external point P, and consider one of the 2 tangents possible through point P.
Does it even matter if tangent is a line, line-segment or ray? I mean, with tangent we are quite flexible, we treat them as it deems necessary. But, is there a fixed definition of tangent that attributes it to the one of 3 possibilities?
Edit : I discussed this question with my friends and a few teachers. Here is the statistic - Most of them seem to agree on tangent being a 'ray'. 'Line' is also a good choice. But almost nobody seems to go with 'line segment'. Personally, I prefer line segment because it gives us 2 informations - first, the origination point P and second, the end point (which lies on curve).
1 Answer
Regarding your informal question, I think we don't have a formal classification on whether a tangent is a line, or a ray, or a line segment. All we can do is to roughly guess the type of that “line” by considering its associated description.
The red line, $\alpha$, is a tangent to the circle and touches it at A. That tangent is a line.
The blue tangent pair, PR and PS, is the tangents to the circle from the external point P. It should be regarded as rays generated from P (provided the dotted parts have no significance).
We also interpret The length of the tangent QT is the length of a line- segment. Of course, PR and PS are also line-segments.
