Titu Andreescu 106 Geometry Problems Pdf 2021 May 2026

You might think geometry books don't need updates. Wrong. The 2021 edition of 106 Geometry Problems introduced three major improvements:

Thus, searching for "titu andreescu 106 geometry problems pdf 2021" specifically (instead of a generic older PDF) is the correct strategy for serious learners.

The 2021 edition follows a clean, effective layout: titu andreescu 106 geometry problems pdf 2021

The difficulty is not strictly increasing. Problem 1 might be easy (AIME #10), while Problem 48 could be IMO 2008 #1 (a known killer). The authors intentionally shuffle difficulty to simulate a real contest—you never know what comes next.

Let $ABC$ be an acute triangle with orthocenter $H$. Let $M$ be the midpoint of $BC$. The circle with diameter $AH$ meets the circumcircle of $ABC$ again at $N$. Prove that $M$, $N$, and the midpoint of $AH$ are collinear. You might think geometry books don't need updates

This requires recognizing that $N$ is the antipode of something, then employing nine-point circle properties.

Problem 42: Let $ABC$ be a triangle with orthocenter $H$. Prove that the reflections of $H$ across the sides of $triangle ABC$ lie on the circumcircle of $ABC$. Thus, searching for "titu andreescu 106 geometry problems

Problem 89: (Inversion) Four circles are tangent to each other externally. Show that the four tangency points lie on a circle.