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A imaginary line that follows the curve of the earth the shortest distance between two points on a globe?
... is called a Great Circle arc.
What is meant by tangent to a curve at a point?
It is a straight line that touches the curve such that the line is perpendicular to the radius of the curve at the point of contact.
What is the name given to a straight line that touches a curve?
In geometry a straight line that touches a curve is called a tangent.
Do a straight line and a curved line form avertex at its joining point?
A tangent at that point where a straight line just touches a curve and a secant line when the straight line bisects the curve.
What is the shortest distance between a straight line and a curve?
If you translate (move without rotation) a copy of the line towards the curve, the first point where the line touches the curve (the tangent to the curve with the slope of the original line) will be the point on the curve closest to the line. Draw a connecting line from this tangent point to the original line, intersecting that original line at right angles. Measure the connecting segment. It is the shortest distance. Vector analysis will give a mathematically strict solution, I do not have the ability to explain this in sufficient detail.
