In triangle ABC, let I be the incenter and Γ be the circumcircle. Extend AI to intersect the circle at L. Show that L is the circumcenter of triangle BIC

OdrogMath Apr 30, 2022

#1**+1 **

This is called the incenter-excenter lemma and is commonly used in olympiad geometry. Its proof is fairly simple. See this proof done by Evan Chen from Taiwan: https://web.evanchen.cc/handouts/Fact5/Fact5.pdf

MaxWong May 2, 2022