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