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
Category: Problem Solving
What leads to success at math contests?
Updated version of generic advice post: Platitudes v3. I think this is an important question to answer, not the least of reasons being that understanding how to learn is extremely useful both for teaching and learning. [1] About a year ago [2], I posted my thoughts on what the most important things were in math… Continue reading What leads to success at math contests?
Writing Olympiad Geometry
I always wondered whether I could generate olympiad geometry problems by simply drawing lines and circles at random until three lines looked concurrent, four points looked concyclic, et cetera. From extensive experience you certainly get the feeling that this ought to be the case -- there are tons and tons of problems out there but… Continue reading Writing Olympiad Geometry
Constructing Parallelograms
This is a reflection of a talk I gave today. Hopefully these reflections (a) help me give better talks, and (b) help out some others. Today I was worked from 6PM-8PM with the Intermediate group at the Berkeley Math Circle, middle school students maybe one or two standard deviations above the average honors student. My… Continue reading Constructing Parallelograms
Power Overwhelming 