MathNet 2023-part-02 — 191 problems (EN–VI) Question 16

Let $ABC$ be a triangle isosceles at $A$, $O$ the centre of its circumcircle and $I$ the centre of its incircle. The line through $I$ parallel to $(AB)$ meets $(AC)$ at $D$. Show that $(CI)$ and $(DO)$ are perpendicular.