Question 28
The incircle of a non-isosceles triangle $\triangle ABC$ has centre $I$ and touches $BC$ and $CA$ at $D$ and $E$, respectively. Let $H$ be the orthocentre of $\triangle ABI$, let $K$ be the intersection of $AI$ and $BH$, and let $L$ be the intersection of $BI$ and $AH$. Prove that the circumcircles of $\triangle DKH$ and $\triangle ELH$ intersect on the incircle of $\triangle ABC$.
