Problem 50: Nice geometry problem

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Joined: Mar 10, 2015

by henderson, Sep 27, 2016, 1:34 PM

$\color{red}\bf{Problem \ 50}$ Let $ABC$ be a triangle and $I$ its incenter. $D, E$ and $F$ are the contact points of the sides $BC, CA$ and $AB$ with the incircle, respectively. Let $\ell$ be a line passing through $B$ and parallel to $CA,$ and $S=\ell \cap FE.$ Define $X$ as the intersection point of $SC$ and $AB.$ Show that $\angle AIX=90^\circ.$