Arc Tangent Point

[SanKul]

Does the intersection of tangents at two end points (tangent point) have any mathematical significance? Does it have any specific properties related to arc? Is it formally defined as some property / attribute of arc?

 

[Deleted member 4993]

Does the intersection of tangents at two end points (tangent point) have any mathematical significance? Does it have any specific properties related to arc? Is it formally defined as some property / attribute of arc?

If those are tangents to a CIRCLE - then those are related.

For a general curve, specific relationship s may be derived.

 

[pka]

Does the intersection of tangents at two end points (tangent point) have any mathematical significance? Does it have any specific properties related to arc? Is it formally defined as some property / attribute of arc?

It is very difficult to know exactly what your question is asking. If two tangents from the same point to a circle determine major and a minor arcs of the circle. The sum of measures of the two arcs is the circumference of the circle. One-half the difference between the measure of the major arc and the measure minor arc is equal to the measure of angle at the external point.

 

[SanKul]

It is not a circle but an arc. And two different tangents are drawn from the two end points of the arc. These tangents intersect. I hope I am more clear now.

 

[Otis]

It is not a circle but an arc

Hi SanKul. In general mathematics, an arc is a portion of any smooth curve (eg: circular, parametric, vector, sinusoidal, polynomial). In particular, circular arcs are probably most common -- that's why the replys so far reference circles. (Your image looks like a circular arc.)

I can't recall seeing anything special about the intersection point of two tangents (or an arc defined by two tangent points) on non-circular arcs. Perhaps there exist definitions within specialized applications (eg: projections in parabolic optics, tower height broadcasting in local topography, surveying, etc), but as far as "pure" math properties go, I'm drawing a blank for generalized arcs.

If you'd like to start exploring with circular arcs, try googling keywords properties of intersecting tangent lines.

 

[SanKul]

Hello Otis, thank you for detailed explanation. It was helpful.