Question 96
Let $ABC$ be a triangle with $AB \lt AC$ inscribed in $(O)$. The tangent line at $A$ of $(O)$ cuts $BC$ at $D$. Take $H$ as the projection of $A$ on $OD$ and $E$, $F$ as projections of $H$ on $AB$, $AC$. Suppose that $EF$ cuts $(O)$ at $R$, $S$. Prove that $(HRS)$ is tangent to $OD$.