## Japanese EGMO is published!

I'm happy to thank 日本評論社 and their team (Fuma Hirayama, Yuki Kumagae, Taiyo Kodama, Ayato Shukuta, among others) for making the Japanese translation a reality. As well as tripling the length of the errata PDF :) This marks the second translation of the EGMO textbook (a Chinese translation was published a while ago as well… Continue reading Japanese EGMO is published!

## Undergraduate Math 011: a firsT yeaR coursE in geometrY

tl;dr I parodied my own book, download the new version here. People often complain to me about how olympiad geometry is just about knowing a bunch of configurations or theorems. But it recently occurred to me that when you actually get down to its core, the amount of specific knowledge that you need to do… Continue reading Undergraduate Math 011: a firsT yeaR coursE in geometrY

## New oly handout: Constructing Diagrams

I've added a new Euclidean geometry handout, Constructing Diagrams, to my webpage. Some of the stuff covered in this handout: Advice for constructing the triangle centers (hint: circumcenter goes first) An example of how to rearrange the conditions of a problem and draw a diagram out-of-order Some mechanical suggestions such as dealing with phantom points… Continue reading New oly handout: Constructing Diagrams

## Revisiting arc midpoints in complex numbers

1. Synopsis One of the major headaches of using complex numbers in olympiad geometry problems is dealing with square roots. In particular, it is nontrivial to express the incenter of a triangle inscribed in the unit circle in terms of its vertices. The following lemma is the standard way to set up the arc midpoints… Continue reading Revisiting arc midpoints in complex numbers

## Some Advice for Olympiad Geometry

I know some friends who are fantastic at synthetic geometry. I can give them any problem and they'll come up with an incredibly impressive synthetic solution. I also have some friends who are very bad at synthetic geometry, but have such good fortitude at computations that they can get away with using Cartesian coordinates for… Continue reading Some Advice for Olympiad Geometry

## Constructing the Tangent and Cotangent Space

This one confused me for a long time, so I figured I should write this down before I forgot again. Let $latex {M}&fg=000000$ be an abstract smooth manifold. We want to define the notion of a tangent vector to $latex {M}&fg=000000$ at a point $latex {p \in M}&fg=000000$. With that, we can define the tangent… Continue reading Constructing the Tangent and Cotangent Space

## The Mixtilinear Incircle

This blog post corresponds to my newest olympiad handout on mixtilinear incircles. My favorite circle associated to a triangle is the $latex {A}&fg=000000$-mixtilinear incircle. While it rarely shows up on olympiads, it is one of the richest configurations I have seen, with many unexpected coincidences showing up, and I would be overjoyed if they become… Continue reading The Mixtilinear Incircle

## Three Properties of Isogonal Conjugates

In this post I'll cover three properties of isogonal conjugates which were only recently made known to me. These properties are generalization of some well-known lemmas, such as the incenter/excenter lemma and the nine-point circle. 1. Definitions Let $latex {ABC}&fg=000000$ be a triangle with incenter $latex {I}&fg=000000$, and let $latex {P}&fg=000000$ be any point in… Continue reading Three Properties of Isogonal Conjugates