A modern monograph on olympiad geometry
In competitive mathematics, geometry is often perceived by students as a chaotic collection of messy intersections and phantom points, where auxiliary lines and constructions occur purely by luck. Beyond the Incenter dismantles this misconception, presenting synthetic geometry as a rigorous, systematic, and highly structured discipline.
Authored for the ambitious student bridging the gap between standard high school curricula and elite-level competitions, this textbook synthesizes classical theorems with modern methods. From the foundational properties of the triangle's five centers to advanced topics like projective geometry and spiral similarity, the text guides readers through the exact techniques required to conquer IMO-caliber configurations.
Why I wrote this book: the geometry gap
Having analysed UKMT markers' reports from the last decade, something alarms me: geometry is consistently the least-attempted and most poorly answered section. The markers explicitly note that geometry questions are "one of the least attempted by candidates," and constantly complain that students rely on "algebraic proof with no reference to the geometrical justifications."
The reason for this is simple: modern high school syllabuses have largely stripped out classical geometry. I see this at my own school. Out of over 1,000 students, only three know Menelaus's Theorem, and exactly two know how to use a complete quadrilateral. Because students lack these core geometric tools, they default to Cartesian coordinate or trigonometric bashes in competitions. As the markers point out, this usually leads to pages of algebra, which are highly prone to errors.
I wrote Beyond the Incenter to fix this specific gap. There are very few resources that bridge the gap from A-Level math to that elite standard. The goal of this book is to show that Olympiad geometry isn't about guessing "lucky" lines. By breaking down methods like projective geometry, radical axes, and spiral similarity, it provides students with a reliable, systematic approach to problems that otherwise look impossible.
Errata
No corrections have been submitted yet. The current Amazon version is V1.0. If you spot a typo, a logical gap or a misaligned diagram, please open an issue on GitHub.
Try the Geometry Lab to see the triangle's centres move, or browse more olympiad resources.