Titu Andreescu 106 Geometry Problems Pdf May 2026
From the book (paraphrased):
"Let ABC be a triangle with orthocenter H. Let M be the midpoint of BC. Let the circle with diameter AH meet the circumcircle of ABC again at point X. Prove that points X, M, and H are collinear."
This problem is a perfect example of the book's style: It looks impossible at first, but after realizing that X is the antipode of something, the solution unfolds like a flower. The solution in the PDF walks you through the radical axis theorem and Euler circle properties in three clear lines.
Published by XYZ Press (a publisher specializing in elite contest preparation), this volume is not a textbook in the traditional sense. It contains minimal theory and no step-by-step re-teaching of basic theorems. Instead, it is a curated collection of problems used at the prestigious AwesomeMath Summer Program. titu andreescu 106 geometry problems pdf
The problems are divided into three distinct parts:
The book is not merely a collection of problems; it is a structured pedagogical tool. It is generally divided into two distinct sections:
The Problem Set: The heart of the book is the collection of 106 distinct problems. These range from accessible exercises suitable for beginners to complex constructions that have appeared in prestigious competitions like the USAMO (USA Mathematical Olympiad) and the IMO. The problems are arranged by topic rather than difficulty, allowing students to immerse themselves in specific techniques. From the book (paraphrased):
Open the PDF to a random problem between #1 and #50. Set a timer for 90 minutes. Use only a blank sheet of paper, a compass, and a ruler (or GeoGebra for checking, not solving). Do not look at the solution. Write down every dead end. This frustration is the molecule of learning.
Unlike standard textbooks that teach theorems first and then provide drills, this book is a problem-solving workshop. It assumes you already know the basics: similar triangles, cyclic quadrilaterals, Power of a Point, and elementary trigonometry.
The "106" refers to the exact number of carefully curated problems. The book is structured into two main parts: "Let ABC be a triangle with orthocenter H
Many students confuse this volume with Andreescu’s other famous work, 103 Trigonometry Problems. The distinction is critical:
The problems are not random contest leftovers. They are hand-picked from the curriculum of the AwesomeMath Summer Program—a training camp for elite middle and high school students aiming for the IMO. If a problem made it into this book, it is guaranteed to have a non-trivial "aha!" moment.