Chord Inverses of Real-Valued Parametric Functions
It is commonly known from elementary geometry that if a point P is exterior to a circle, there are exactly two lines tangent to the circle which intersect at P. Consequently, the points of tangency between the circle and these lines identify a specific chord of the circle, which in turn identifies a distinct line in the plane. If we let P traverse some parametric function f(t), we obtain a series of chord-containing lines which correspond to a series of points belonging to f(t). In this paper, we consider these lines to be the tangent lines of some unknown parametric function g(t) which we call the chord inverse of f(t). We also derive chord inverses of various functions and discuss both their general and specific properties.