Some Generalizations of a Geometric Problem from USA TSTST

Research Question

How can the 2016 USA TSTST geometry problem be extended to broader configurations using synthetic and projective geometry?

Abstract

In this paper, we present several extensions to a beautiful and important problem from the 2016 USA TSTST. This problem itself serves as an extremely interesting illustration of the method using power of a point and the radical axis in plane geometry. In our proof for the extensions problems, in addition to combining the method of power of a point and the radical axis, we also utilize the cross ratio of points and pencils of lines along with central projection, which are important tools of projective geometry.

What This Paper Does

The paper develops generalizations of the original problem. Its proofs combine power of a point and radical axes with cross ratios of points and pencils of lines, together with central projection.

My Contribution

• Generalized the original competition problem to broader geometric configurations.
• Provided rigorous synthetic geometry proofs for all generalizations.
• Drafted the paper.