The equal tangents problem

TL;DR

This paper explores a geometric problem involving a moving point around a plane oval, demonstrating the possibility of maintaining unequal tangent segment lengths at all times.

Contribution

It constructs the first known example of a plane oval allowing a path where tangent segments from a moving point are always unequal.

Findings

Existence of such an oval is proven.

Explicit example of the oval is provided.

The problem's geometric constraints are analyzed.

Abstract

Given a plane oval, is it possible to go around it so that, at all times, the two tangent segments to the oval from the moving point have unequal lengths? In this note we construct an example of such an oval.