In triangle $ABC$, let $I$ be the incentre. Let $H$ be the orthocentre of triangle $BIC$. Show that $AH$ is parallel to $BC$ if and only if $H$ lies on the circle with diameter $AI$.
Source: Canada Repêchage 2024/7a CMOQR
Tags: geometry, orthocenter, incenter
In triangle $ABC$, let $I$ be the incentre. Let $H$ be the orthocentre of triangle $BIC$. Show that $AH$ is parallel to $BC$ if and only if $H$ lies on the circle with diameter $AI$.