# Chord Inverses of Real-Valued Parametric Functions

### Abstract

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.

**Minnesota Journal of Undergraduate Mathematics**, [S.l.], v. 5, n. 1, aug. 2019. ISSN 2378-5810. Available at: <https://mjum.math.umn.edu/index.php/mjum/article/view/112>. Date accessed: 19 sep. 2019.