Problem - 04 - National Math Camp 2021 Mock Exam - "Angle bisector, spiral similarity etc."
Posted: Thu May 13, 2021 12:25 am
Let $ABC$ be a triangle such that $AB < AC$. Let $D$ be a point on $AC$ such that $CD = BD$. The line parallel to $BC$ through $D$ meet the minor arc $AB$ of $\odot ABC$ at $E$. Let $I, J$ be the incenters of $\triangle ADE$ and $\triangle BDE$ respectively. Prove that the internal angle bisector of $\angle AEB$ is perpendicular to $IJ$.